Prime Factors of 312

Steps to find Prime Factors of 312 by Division Method

To find the primefactors of 312 using the division method, follow these steps:

• Step 1. Start dividing 312 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 312, which is 2. Divide 312 by 2 to obtain the quotient (156).
  312 ÷ 2 = 156
• Step 3. Repeat step 1 with the obtained quotient (156).
  156 ÷ 2 = 78
  78 ÷ 2 = 39
  39 ÷ 3 = 13
  13 ÷ 13 = 1

So, the prime factorization of 312 is, 312 = 2 x 2 x 2 x 3 x 13.

Steps to find Prime Factors of 312 by Factor Tree Method

We can follow the same procedure using the factor tree of 312 as shown below:

So, the prime factorization of 312 is, 312 = 2 x 2 x 2 x 3 x 13.

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 312 are 2 x 2 x 2 x 3 x 13.

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 312 but not a prime factor of 312.

Frequently Asked Questions

• Which is the smallest prime factor of 312?

  Smallest prime factor of 312 is 2.

• Is 312 a perfect square?

  No 312 is not a perfect square.

• What is the prime factorization of 312?

  Prime factorization of 312 is 2 x 2 x 2 x 3 x 13.

• What is prime factorization of 312 in exponential form?

  Prime factorization of 312 in exponential form is 2³ x 3 x 13.

• Is 312 a prime number or a composite number?

  312 is a composite number.

• Which is the largest prime factors of 312?

  The largest prime factor of 312 is 13.

• What is the product of all prime factors of 312?

  Prime factors of 312 are 2 x 2 x 2 x 3 x 13. Therefore, their product is 312.

• What numbers are the prime factors of 312?

  Prime factors of 312 are 2 , 2 , 2 , 3 , 13.

• Is there any even prime factor of 312?

  Yes there is a even prime factor of 312.