118 LearnersLast updated on May 26th, 2025
Is 691 a Prime Number?
The numbers that have only two factors, which are 1 and themselves, are called prime numbers. For encryption, computer algorithms, and barcode generation, prime numbers are used. In this topic, we will be discussing whether 691 is a prime number or not.
Is 691 a Prime Number?
There are two types of numbers, mostly — prime numbers and composite numbers, depending on the number of factors. A prime number is a natural number that is divisible only by 1 and itself. For example, 3 is a prime number because it is divisible by 1 and itself. A composite number is a positive number that is divisible by more than two numbers. For example, 6 is divisible by 1, 2, 3, and 6, making it a composite number. Prime numbers follow a few properties like: - Prime numbers are positive numbers always greater than 1. - 2 is the only even prime number. - They have only two factors: 1 and the number itself. - Any two distinct prime numbers are co-prime numbers because they have only one common factor, which is 1. To determine if 691 is a prime number, we need to check its divisors.
Why is 691 Not a Prime Number?
The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 691 has more than two factors, it is not a prime number. Several methods are used to distinguish between prime and composite numbers: - Counting Divisors Method - Divisibility Test - Prime Number Chart - Prime Factorization
Using the Counting Divisors Method
The method in which we count the number of divisors to categorize numbers as prime or composite is called the counting divisors method. Based on the count of the divisors, we categorize prime and composite numbers. - If there is a total count of only 2 divisors, then the number is prime. - If the count is more than 2, then the number is composite. Let’s check whether 691 is prime or composite. Step 1: All numbers are divisible by 1 and themselves. Step 2: Divide 691 by 2, 3, 5, 7, and other numbers up to the square root of 691. Step 3: 691 is divisible by 13 (691 ÷ 13 = 53), indicating that it has more than two divisors. Since 691 has more than 2 divisors, it is a composite number.
Using the Divisibility Test Method
We use a set of rules to check whether a number is divisible by another number completely or not. It is called the Divisibility Test Method. - Divisibility by 2: 691 is odd, so it is not divisible by 2. - Divisibility by 3: The sum of the digits in 691 is 16. Since 16 is not divisible by 3, 691 is not divisible by 3. - Divisibility by 5: The unit’s place digit is 1. Therefore, 691 is not divisible by 5. - Divisibility by 7: Perform calculations to determine divisibility by 7, but 691 is not divisible by 7. - Divisibility by 13: 691 is divisible by 13, confirming it has more than two factors. Since 691 is divisible by 13, it has more than two factors. Therefore, it is a composite number.
Using Prime Number Chart
The prime number chart is a tool created by using a method called “The Sieve of Eratosthenes.” In this method, we follow these steps: Step 1: Write numbers from 1 to 1000 in rows and columns. Step 2: Leave 1 without coloring or crossing, as it is neither prime nor composite. Step 3: Mark 2 because it is a prime number and cross out all multiples of 2. Step 4: Mark 3 because it is a prime number and cross out all multiples of 3. Step 5: Repeat this process until reaching the desired range. Through this process, we have a list of prime numbers. Since 691 is not on this list, it is a composite number.
Using the Prime Factorization Method
Prime factorization is a process of breaking down a number into prime factors. Then multiply those factors to obtain the original number. Step 1: We can write 691 as 13 × 53. Step 2: Both 13 and 53 are prime numbers. Step 3: Hence, the prime factorization of 691 is 13 × 53.
Common Mistakes to Avoid When Determining if 691 is Not a Prime Number
Children might have some misconceptions about prime numbers when they are learning about them. Here are some mistakes that might be made by children.
Mistake 1
Assuming That All Odd Numbers Are Prime
Solution: Children have an assumption that all odd numbers are prime numbers. They should be taught that except for 2, most prime numbers are odd, but not all odd numbers are prime. For example, 15 is an odd number, but it has more than two factors, which makes it a composite number.
Mistake 2
Confusing 1 as a Prime Number
Children should know the definition of a prime number as having only two factors. But 1 has only one factor, which is itself. 1 is a unique number that is neither a prime nor a composite number.
Mistake 3
Depending Too Much on Memorization
Children rely on memorizing the prime numbers. But they might forget whether 29 or 39 is prime. To avoid these kinds of problems, children should have knowledge of divisibility rules rather than depending on memorization.
Mistake 4
Applying Divisibility Rules Incorrectly
When children divide a number by another number, they might make mistakes in calculation. For example, children might make mistakes while dividing 72 by 3. Teach them shortcuts, like if the sum of the digits of a number is divisible by 3, then the number is also divisible by 3.
Mistake 5
Assuming That Negative Numbers Are Prime
Children might think that negative numbers can also be prime numbers. For example, they might apply the divisibility rule of 2 for -48 to check whether it is prime or not. They need to know that prime numbers are positive numbers greater than 1.
FAQ on is 691 a Prime Number?
1.Is 691 a perfect square?
2.What is the sum of the divisors of 691?
3.What are the factors of 691?
4.What are the closest prime numbers to 691?
5.What is the prime factorization of 691?
6.How can children in Thailand use numbers in everyday life to understand Is 691 a Prime Number??
7.What are some fun ways kids in Thailand can practice Is 691 a Prime Number? with numbers?
8.What role do numbers and Is 691 a Prime Number? play in helping children in Thailand develop problem-solving skills?
9.How can families in Thailand create number-rich environments to improve Is 691 a Prime Number? skills?
Important Glossaries for "Is 691 a Prime Number"
1. Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 691 is a composite number because it is divisible by 1, 13, 53, and 691. 2. Prime numbers: Natural numbers greater than 1 that are divisible only by 1 and themselves are called prime numbers. For example, 13 is a prime number. 3. Divisibility: A number's ability to be divided by another number without leaving a remainder. For example, 12 is divisible by 3. 4. Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 691 is 13 × 53. 5. Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.
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About BrightChamps in Thailand
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.
Fun Fact
: She loves to read number jokes and games.
