Prime Factors of 972

Steps to find Prime Factors of 972 by Division Method

To find the primefactors of 972 using the division method, follow these steps:

• Step 1. Start dividing 972 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 972, which is 2. Divide 972 by 2 to obtain the quotient (486).
  972 ÷ 2 = 486
• Step 3. Repeat step 1 with the obtained quotient (486).
  486 ÷ 2 = 243
  243 ÷ 3 = 81
  81 ÷ 3 = 27
  27 ÷ 3 = 9
  9 ÷ 3 = 3
  3 ÷ 3 = 1

So, the prime factorization of 972 is, 972 = 2 x 2 x 3 x 3 x 3 x 3 x 3.

Steps to find Prime Factors of 972 by Factor Tree Method

We can follow the same procedure using the factor tree of 972 as shown below:

So, the prime factorization of 972 is, 972 = 2 x 2 x 3 x 3 x 3 x 3 x 3.

How do you define Prime Factors of a number?

Prime numbers, in mathematics are all those natural numbers greater than 1 that have exactly 2 factors which are 1 and the number itself. When we express any number as the product of these prime numbers than these prime numbers become prime factors of that number. Eg- Prime Factors of 972 are 2 x 2 x 3 x 3 x 3 x 3 x 3.

Properties of Prime Factors

• For any given number there is one and only one set of unique prime factors.
• Any number can have only 1 even prime factor and that is number 2.
• Two prime factors are always coprime to each other.
• 1 is the factor of any given number, but 1 is neither a prime number nor a composite number. So, 1 is the factor of 972 but not a prime factor of 972.

Frequently Asked Questions

• Which is the smallest prime factor of 972?

  Smallest prime factor of 972 is 2.

• What is the prime factorization of 972?

  Prime factorization of 972 is 2 x 2 x 3 x 3 x 3 x 3 x 3.

• What are the factors of 972?

  Factors of 972 are 1 , 2 , 3 , 4 , 6 , 9 , 12 , 18 , 27 , 36 , 54 , 81 , 108 , 162 , 243 , 324 , 486 , 972.

• Is 972 a prime number or a composite number?

  972 is a composite number.

• Is 972 a prime number?

  false, 972 is not a prime number.

• Which is the largest prime factors of 972?

  The largest prime factor of 972 is 3.

• What is the sum of all prime factors of 972?

  Prime factors of 972 are 2 x 2 x 3 x 3 x 3 x 3 x 3. Therefore, their sum is 19.

• What numbers are the prime factors of 972?

  Prime factors of 972 are 2 , 2 , 3 , 3 , 3 , 3 , 3.

• What is the sum of all odd prime factors of 972?

  Prime factors of 972 are 2 , 2 , 3 , 3 , 3 , 3 , 3, out of which 3 , 3 , 3 , 3 , 3 are odd numbers. So, the sum of odd prime factors of 972 is 3 + 3 + 3 + 3 + 3 = 15.