Last updated on July 1st, 2025
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 150 to 200.
A prime number is a natural number with no positive factors other than 1 and the number itself. And the prime number can only be evenly divisible by 1 and the number itself. Here are some basic properties of prime numbers:
A prime number chart is a table showing the prime numbers in increasing order. The chart simply 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, fundamental theorem of arithmetic.
The list of all prime numbers from 150 to 200 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 150 to 200 include 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, and 199.
Prime numbers and odd numbers are the numbers that are only divisible by 1 and the number itself. It 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 2 all prime numbers are considered as the set of odd numbers.
Prime numbers are a set of natural numbers that can only be divided by 1 and the number itself. Here are the two important ways to find whether a number is prime or not.
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 meant to be a prime number.
For example: To check whether 167 is a prime number,
Step 1: 167 ÷ 2 = 83.5 (remainder ≠ 0)
Step 2: 167 ÷ 3 = 55.66 (remainder ≠ 0)
Step 3: 167 ÷ 5 = 33.4 (remainder ≠ 0)
Since no divisors are found, 167 is a prime number.
The Prime factorization method is the process of breaking down the composite number into the product of its prime factors. The method of prime factorization helps to identify the prime numbers up to 200 by building the smallest blocks of any given number.
For example: The prime factorization of 180: Let's break it down into the smallest prime numbers until it can’t divide anymore.
Step 1: 180 ÷ 2 = 90
Step 2: Now, we divide 90, 90 ÷ 2 = 45
Step 3: Now take 45, since 45 ends in 5 divide the number with 5 45 ÷ 5 = 9
Step 4: Take 9, since 9 is divisible by 3, 9 ÷ 3 = 3
Step 5: At last, take 3. 3 ÷ 3 = 1
Therefore, the prime factorization of 180 is: 180 = 2² × 3² × 5.
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, and 7. 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 150 to 200. Then start with the first prime number, 2. Mark all the multiples of 2 as non-prime.
Repeat the process for the next unmarked prime number and continue until you reach the square root of 200, approximately 14.14. The remaining unmarked numbers are the prime numbers.
While working with the prime numbers 150 to 200 children might encounter some errors or difficulties. We have many solutions to resolve those problems. Here are some given below:
Is 197 a prime number?
Yes, 197 is a prime number.
The square root of 197 is √197 = 14.035, we check divisibility by primes less than 14.035. (2, 3, 5, 7, 11, 13).
197 ÷ 2 = 98.5
197 ÷ 3 = 65.666
197 ÷ 5 = 39.4
197 ÷ 7 = 28.142
197 ÷ 11 = 17.909
Since 197 is not divisible by any of these numbers, 197 is a prime number.
A website requires a password that is the largest prime number between 150 and 200. Which prime number is that?
199 is the largest prime number between 150 and 200.
Prime numbers are natural numbers that are greater than 1 and have no divisors other than 1 and the number itself.
The prime numbers between 150 and 200 are 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199. 199 is the largest prime number in this range, therefore the password is 199.
A teacher challenges her students: Find the prime numbers that are closest to 175 but less than 175.
173 is the prime number which is closest to 175.
173 is a prime number because it is only divisible by 1 and the number itself. And the next prime number after 173 is 179, which is greater than 175.
Therefore, the prime number closest to 175 and less than 175 is 173.
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.
: She loves to read number jokes and games.