Prime Factors of 462

Steps to find Prime Factors of 462 by Division Method

To find the primefactors of 462 using the division method, follow these steps:

• Step 1. Start dividing 462 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 462, which is 2. Divide 462 by 2 to obtain the quotient (231).
  462 ÷ 2 = 231
• Step 3. Repeat step 1 with the obtained quotient (231).
  231 ÷ 3 = 77
  77 ÷ 7 = 11
  11 ÷ 11 = 1

So, the prime factorization of 462 is, 462 = 2 x 3 x 7 x 11.

Steps to find Prime Factors of 462 by Factor Tree Method

We can follow the same procedure using the factor tree of 462 as shown below:

So, the prime factorization of 462 is, 462 = 2 x 3 x 7 x 11.

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 462 are 2 x 3 x 7 x 11.

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 462 but not a prime factor of 462.

Frequently Asked Questions

• Which is the smallest prime factor of 462?

  Smallest prime factor of 462 is 2.

• Is 462 a perfect square?

  No 462 is not a perfect square.

• What is the prime factorization of 462?

  Prime factorization of 462 is 2 x 3 x 7 x 11.

• What are the factors of 462?

  Factors of 462 are 1 , 2 , 3 , 6 , 7 , 11 , 14 , 21 , 22 , 33 , 42 , 66 , 77 , 154 , 231 , 462.

• What is the product of all prime factors of 462?

  Prime factors of 462 are 2 x 3 x 7 x 11. Therefore, their product is 462.

• What numbers are the prime factors of 462?

  Prime factors of 462 are 2 , 3 , 7 , 11.

• What is the sum of all odd prime factors of 462?

  Prime factors of 462 are 2 , 3 , 7 , 11, out of which 3 , 7 , 11 are odd numbers. So, the sum of odd prime factors of 462 is 3 + 7 + 11 = 21.

• Is there any even prime factor of 462?

  Yes there is a even prime factor of 462.

• What is the product of all odd prime factors of 462?

  Prime factors of 462 are 2 , 3 , 7 , 11, out of which 3 , 7 , 11 are odd numbers. So, the product of odd prime factors of 462 is 3 x 7 x 11 = 231.