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Last updated on July 1st, 2025

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Prime Numbers 700 to 800

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The natural numbers greater than 1 are called prime numbers. Prime numbers have only two factors, 1 and the number itself. Besides math, we use prime numbers in many fields, such as securing digital data, radio frequency identification, etc. In this topic, we will learn about the prime numbers 700 to 800.

Prime Numbers 700 to 800 for Australian Students
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Prime Numbers 700 to 800

A prime number is a natural number with no positive factors other than 1 and the number itself. A prime number can only be evenly divisible by 1 and the number itself. Here are some basic properties of prime numbers:

 

  • Every number greater than 1 is divisible by at least one prime number.

 

  • Two prime numbers are always relatively prime to each other.

 

  • Every even positive integer greater than 2 can be written as the sum of two prime numbers.

 

  • Every composite number can be uniquely factored into prime factors.

 

  • Except for 2, all prime numbers are odd; 2 is the only even prime number.
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Prime Numbers 700 to 800 Chart

A prime number chart is a table showing the prime numbers in increasing order. The chart includes all the prime numbers up to a certain limit for identifying the prime numbers within a range.

 

For kids, it will be less difficult to understand the prime numbers through the chart. The significance of this prime number chart is used in different fields like the foundation of mathematics and the fundamental theorem of arithmetic.

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List of All Prime Numbers 700 to 800

The list of all prime numbers from 700 to 800 provides a comprehensive view of numbers in this range that can only be divided by 1 and the number itself. The prime numbers in the range of 700 to 800 include 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797.

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Prime Numbers - Odd Numbers

Prime numbers and odd numbers are the numbers that are only divisible by 1 and the number itself. They cannot be evenly divisible by 2 or other numbers. 2 is the only even prime number, which divides all the non-prime numbers. Therefore, except for 2, all prime numbers are considered as the set of odd numbers.

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How to Identify Prime Numbers 700 to 800

Prime numbers are a set of natural numbers that can only be divided by 1 and the number itself. Here are two important ways to find whether a number is prime or not.

 

By Divisibility Method:

 

To find whether a number is prime or not, we use the divisibility method to check. If a number is divisible by 2, 3, or 5, then it will result in a non-prime number. Prime numbers are only divisible by 1 and itself, so if a number is divisible by the number itself and 1, it is a prime number.

 

For example: To check whether 727 is a prime number,

 

Step 1: 727 ÷ 2 = 363.5 (remainder ≠ 0)

 

Step 2: 727 ÷ 3 = 242.33 (remainder ≠ 0)

 

Step 3: 727 ÷ 5 = 145.4 (remainder ≠ 0)

 

Since no divisors are found, 727 is a prime number.

 

By Prime Factorization Method:

 

The prime factorization method is the process of breaking down a composite number into the product of its prime factors. The method of prime factorization helps to identify the prime numbers up to 800 by building the smallest blocks of any given number.

 

For example: The prime factorization of 800: Let's break it down into the smallest prime numbers until it can’t divide anymore.

 

Step 1: 800 ÷ 2 = 400

 

Step 2: Now, we divide 400, 400 ÷ 2 = 200

 

Step 3: Now take 200, 200 ÷ 2 = 100

 

Step 4: Take 100, 100 ÷ 2 = 50

 

Step 5: Take 50, 50 ÷ 2 = 25

 

Step 6: At last, take 25, 25 ÷ 5 = 5

 

Step 7: Finally, take 5, 5 ÷ 5 = 1 (since 5 is a prime number, and dividing by 5 gives 1)

 

Therefore, the prime factorization of 800 is: 800 = 25 × 52.

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Rules for Identifying Prime Numbers 700 to 800

Rule 1: Divisibility Check: Prime numbers are natural numbers that are greater than 1 and have no divisors other than 1 and the number itself. In the divisibility check rule, we check whether the prime number is divisible by 2, 3, 5, 7, 11, 13, 17, 19, or 23. If it's divisible by these numbers, then it's not a prime number.

 

Rule 2: Prime Factorization: In this prime factorization method, we break down all the numbers into their prime factors, showing them as the product of prime numbers.

 

Rule 3: Sieve of Eratosthenes Method: The method, sieve of Eratosthenes, is an ancient algorithm used to find all prime numbers up to a given limit. First, we list all the numbers from 700 to 800. Then start with the first prime number, 701. Mark all the multiples of 701 as non-prime.

 

Repeat the process for the next unmarked prime number and continue until you reach the square root of 800, approximately 28.28. The remaining unmarked numbers are the prime numbers.

 

Tips and Tricks for Prime Numbers 700 to 800

 

Use common shortcuts to memorize the prime numbers. 701, 709, 719, 727, 733, 739, 743, 751, and 757 use these numbers as reference. Practice using the method of Sieve of Eratosthenes efficiently. Numbers like 704, 708, 716, 728, and 736 are never meant to be prime. Knowing the common powers of numbers helps in avoiding unnecessary checks.

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Common Mistakes and How to Avoid Them in Prime Numbers 700 to 800

While working with the prime numbers 700 to 800, children might encounter some errors or difficulties. We have many solutions to resolve those problems. Here are some given below:

Mistake 1

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Confusing composite numbers with prime numbers.

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A prime number has exactly 2 divisors: 1 and the number itself. Remember that composite numbers have more than 2 divisors. For example: 728 is not a prime number because it has more than 2 divisors.

Mistake 2

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Including 1 as a prime number.

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Always remember that primes are greater than 1. 1 is not a prime number because it has only one divisor: itself.

Mistake 3

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Not efficiently using the prime checking method.

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Practice using the method of Sieve of Eratosthenes efficiently, or check divisibility by primes up to the square root of the number. For example: while checking the divisibility of 781, stop once you reach √781.

Mistake 4

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Not realizing about the primes in the larger prime range.

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Keep on practicing identifying the larger primes, as it helps to sharpen the skills of children. The usage of the method of Sieve of Eratosthenes helps to solve this.

Mistake 5

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Forgetting that multiples of any prime number are not prime.

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Erase all the multiples of known prime numbers as soon as possible. For example: If you're checking numbers up to 800, you don't have to check numbers divisible by 2, 3, 5, or 7 because they are not prime.

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Prime Numbers Examples

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Problem 1

Is 757 a prime number?

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Yes, 757 is a prime number.

Explanation

The square root of 757 is √757 ≈ 27.5, we check divisibility by primes less than 27.5 (2, 3, 5, 7, 11, 13, 17, 19, 23).

 

757 ÷ 2 = 378.5

 

757 ÷ 3 = 252.33

 

757 ÷ 5 = 151.4

 

757 ÷ 7 = 108.14

 

757 ÷ 11 = 68.82

 

Since 757 is not divisible by any of these numbers, 757 is a prime number.

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Problem 2

Annie is trying to open a digital locker with a 3-digit number. The code is the largest prime number under 800. Which prime number will open the lock?

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797 is the 3-digit code of the digital locker and the largest prime number under 800.

Explanation

Prime numbers are natural numbers that are greater than 1 and have no divisors other than 1 and the number itself. The prime numbers under 800 are 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, and so on. 797 is the largest prime number under 800, therefore the code to open the digital locker is 797.

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Problem 3

A teacher challenges her students: Find the prime numbers that are closest to 750 but less than 750.

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743 is the prime number which is closest to 750.

Explanation

743 is a prime number because it is only divisible by 1 and the number itself. And the next prime number after 743 is 751, which is greater than 750. Therefore, the prime number closest to 750 and less than 750 is 743.

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FAQs on Prime Numbers 700 to 800

1.Give some examples of prime numbers.

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2.Explain prime numbers in math.

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3.Is 2 the smallest prime number?

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4.Which is the largest prime number?

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5.Which is the largest prime number in 700 to 800?

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6.How can children in Australia use numbers in everyday life to understand Prime Numbers 700 to 800?

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7.What are some fun ways kids in Australia can practice Prime Numbers 700 to 800 with numbers?

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8.What role do numbers and Prime Numbers 700 to 800 play in helping children in Australia develop problem-solving skills?

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9.How can families in Australia create number-rich environments to improve Prime Numbers 700 to 800 skills?

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Important Glossaries for Prime Numbers 700 to 800

  • Prime numbers: The natural numbers which are greater than 1 and that are divisible by 1 and the number itself. For example: 701, 709, 719, 727, and so on.

 

  • Odd numbers: The numbers that are not divisible by 2 are called odd numbers. All prime numbers except 2 are odd. For example: 701, 709, 719, and so on.

 

  • Composite numbers: Composite numbers are non-prime numbers that have more than 2 factors. For example, 800 is a composite number, and it is divisible by 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 160, 200, 400, and 800.

 

  • Divisibility: A method to check if a number can be divided by another without a remainder. For example, 720 ÷ 5 leaves a remainder, so 720 is not divisible by 5.

 

  • Sieve of Eratosthenes: An ancient algorithm to discover all prime numbers up to a specified integer. It removes multiples of each prime number starting with 2.
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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

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Fun Fact

: She loves to read number jokes and games.

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