Prime Factors of 126

Steps to find Prime Factors of 126 by Division Method

To find the primefactors of 126 using the division method, follow these steps:

• Step 1. Start dividing 126 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 126, which is 2. Divide 126 by 2 to obtain the quotient (63).
  126 ÷ 2 = 63
• Step 3. Repeat step 1 with the obtained quotient (63).
  63 ÷ 3 = 21
  21 ÷ 3 = 7
  7 ÷ 7 = 1

So, the prime factorization of 126 is, 126 = 2 x 3 x 3 x 7.

Steps to find Prime Factors of 126 by Factor Tree Method

We can follow the same procedure using the factor tree of 126 as shown below:

So, the prime factorization of 126 is, 126 = 2 x 3 x 3 x 7.

Introduction to Prime Factors?

In mathematics, prime numbers are defined as all those natural numbers greater than 1 that has only two divisors one being number 1 and the other being the number itself. When we express any number as the products of these prime numbers than these prime numbers become prime factors of that number. Eg- Prime Factors of 126 are 2 x 3 x 3 x 7.

Properties of Prime Factors

• Two prime factors of a given number are always coprime to each other.
• 2 is the only even prime factor any number can have.
• Two prime factors are always coprime to each other.
• 1 is neither a prime number nor a composite number and also 1 is the factor of every given number. So, 1 is the factor of 126 but not a prime factor of 126.

Frequently Asked Questions

• Which is the smallest prime factor of 126?

  Smallest prime factor of 126 is 2.

• Is 126 a perfect square?

  No 126 is not a perfect square.

• What is the prime factorization of 126?

  Prime factorization of 126 is 2 x 3 x 3 x 7.

• What are the factors of 126?

  Factors of 126 are 1 , 2 , 3 , 6 , 7 , 9 , 14 , 18 , 21 , 42 , 63 , 126.

• What is the product of all prime factors of 126?

  Prime factors of 126 are 2 x 3 x 3 x 7. Therefore, their product is 126.

• What numbers are the prime factors of 126?

  Prime factors of 126 are 2 , 3 , 3 , 7.

• What is the sum of all odd prime factors of 126?

  Prime factors of 126 are 2 , 3 , 3 , 7, out of which 3 , 3 , 7 are odd numbers. So, the sum of odd prime factors of 126 is 3 + 3 + 7 = 13.

• Is there any even prime factor of 126?

  Yes there is a even prime factor of 126.

• What is the product of all odd prime factors of 126?

  Prime factors of 126 are 2 , 3 , 3 , 7, out of which 3 , 3 , 7 are odd numbers. So, the product of odd prime factors of 126 is 3 x 3 x 7 = 63.