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Factors of 462

Factors of 462 are numbers that, when multiplied in pairs give the product as 462. There are overall 16 factors of 462 among which 462 is the biggest factor and its prime factors are 2, 3, 7, 11. The sum of all factors of 462 is 1152.

  • All Factors of 462: 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231 and 462
  • Prime Factors of 462: 2, 3, 7, 11
  • Prime Factorization of 462: 21 × 31 × 71 × 111
  • Sum of Factors of 462: 1152
1. What Are the Factors of 462?
2. Factors of 462 by Prime Factorization
3. Factors of 462 in Pairs
4. FAQs on Factors of 462
Factors of 462

What are Factors of 462?

Factors of 462 are pairs of those numbers whose products result in 462. These factors are either prime numbers or composite numbers.

How to Find the Factors of 462?

To find the factors of 462, we will have to find the list of numbers that would divide 462 without leaving any remainder.

  • 462/66 = 7; therefore, 66 is a factor of 462 and 7 is also a factor of 462.
  • 462/154 = 3; therefore, 154 is a factor of 462 and 3 is also a factor of 462.
Similarly we can find other factors. Hence, the factors of 462 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462.

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Factors of 462 by Prime Factorization

The number 462 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 462. The first step is to divide the number 462 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 462 ÷ 2 = 231

Further dividing 231 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 231 by the next smallest prime factor. We stop ultimately if the next prime factor doesn't exist or when we can't divide any further.

So, the prime factorization of 462 can be written as 21 × 31 × 71 × 111 where 2, 3, 7, 11 are prime.

 

Factors of 462 in Pairs

Pair factors of 462 are the pairs of numbers that when multiplied give the product 462. The factors of 462 in pairs are:

  • 1 × 462 = (1, 462)
  • 2 × 231 = (2, 231)
  • 3 × 154 = (3, 154)
  • 6 × 77 = (6, 77)
  • 7 × 66 = (7, 66)
  • 11 × 42 = (11, 42)
  • 14 × 33 = (14, 33)
  • 21 × 22 = (21, 22)

Negative pair factors of 462 are:

  • -1 × -462 = (-1, -462)
  • -2 × -231 = (-2, -231)
  • -3 × -154 = (-3, -154)
  • -6 × -77 = (-6, -77)
  • -7 × -66 = (-7, -66)
  • -11 × -42 = (-11, -42)
  • -14 × -33 = (-14, -33)
  • -21 × -22 = (-21, -22)

NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.

Factors of 462 Solved Examples

  1. Example 1: How many factors are there for 462?

    Solution:

    The factors of 462 are too many, therefore if we can find the prime factorization of 462, then the total number of factors can be calculated using the formula shown below.
    If the prime factorization of the number is ax × by × cz where a, b, c are prime, then the total number of factors can be given by (x + 1)(y + 1)(z + 1).

    Prime Factorization of 462 = 21 × 31 × 71 × 111
    Therefore, the total number of factors are (1 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 2 × 2 × 2 × 2 = 16

  2. Example 2: Find the LCM and Greatest Common Divisor (GCD) of 462 and 27.

    Solution:

    The factors of 462 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462 and factors of 27 are 1, 3, 9, 27.

    Therefore, the LCM of 462 and 27 is 4158 and Greatest Common Divisor (GCD) of 462 and 27 is 3.

  3. Example 3: Find if 6, 11, 14, 42, 66, 154, 375 and 462 are factors of 462.

    Solution:

    When we divide 462 by 375 it leaves a remainder. Therefore, the number 375 is not a factor of 462. All numbers except 375 are factors of 462.

  4. Example 4: Find the product of all the prime factors of 462.

    Solution:

    Since, the prime factors of 462 are 2, 3, 7, 11. Therefore, the product of prime factors = 2 × 3 × 7 × 11 = 462.

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FAQs on Factors of 462

What are the Factors of 462?

The factors of 462 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462 and its negative factors are -1, -2, -3, -6, -7, -11, -14, -21, -22, -33, -42, -66, -77, -154, -231, -462.

What is the Sum of all Factors of 462?

Sum of all factors of 462 = (21 + 1 - 1)/(2 - 1) × (31 + 1 - 1)/(3 - 1) × (71 + 1 - 1)/(7 - 1) × (111 + 1 - 1)/(11 - 1) = 1152

What are the Pair Factors of 462?

The pair factors of 462 are (1, 462), (2, 231), (3, 154), (6, 77), (7, 66), (11, 42), (14, 33), (21, 22).

What is the Greatest Common Factor of 462 and 438?

The factors of 462 and 438 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462 and 1, 2, 3, 6, 73, 146, 219, 438 respectively.

Common factors of 462 and 438 are [1, 2, 3, 6].

Hence, the Greatest Common Factor of 462 and 438 is 6.

How Many Factors of 208 are also common to the Factors of 462?

Since, the factors of 462 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462 and the factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208.
Hence, [1, 2] are the common factors of 462 and 208.

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