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Factors of 456

Factors of 456 are numbers that, when multiplied in pairs give the product as 456. It has total 16 factors of which 456 is the biggest factor and the prime factors of 456 are 2, 3, 19. The sum of all factors of 456 is 1200.

  • All Factors of 456: 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228 and 456
  • Prime Factors of 456: 2, 3, 19
  • Prime Factorization of 456: 23 × 31 × 191
  • Sum of Factors of 456: 1200
1. What Are the Factors of 456?
2. Factors of 456 by Prime Factorization
3. Factors of 456 in Pairs
4. FAQs on Factors of 456
Factors of 456

What are Factors of 456?

Factors of 456 are pairs of those numbers whose products result in 456. These factors are either prime numbers or composite numbers.

How to Find the Factors of 456?

To find the factors of 456, we will have to find the list of numbers that would divide 456 without leaving any remainder.

  • 456/3 = 152; therefore, 3 is a factor of 456 and 152 is also a factor of 456.
  • 456/19 = 24; therefore, 19 is a factor of 456 and 24 is also a factor of 456.
Similarly we can find other factors. Hence, the factors of 456 are 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456.

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Factors of 456 by Prime Factorization

The number 456 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 456. The first step is to divide the number 456 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 456 ÷ 2 = 228
  • 228 ÷ 2 = 114
  • 114 ÷ 2 = 57

Further dividing 57 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 57 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 456 can be written as 23 × 31 × 191 where 2, 3, 19 are prime.

 

Factors of 456 in Pairs

Pair factors of 456 are the pairs of numbers that when multiplied give the product 456. The factors of 456 in pairs are:

  • 1 × 456 = (1, 456)
  • 2 × 228 = (2, 228)
  • 3 × 152 = (3, 152)
  • 4 × 114 = (4, 114)
  • 6 × 76 = (6, 76)
  • 8 × 57 = (8, 57)
  • 12 × 38 = (12, 38)
  • 19 × 24 = (19, 24)

Negative pair factors of 456 are:

  • -1 × -456 = (-1, -456)
  • -2 × -228 = (-2, -228)
  • -3 × -152 = (-3, -152)
  • -4 × -114 = (-4, -114)
  • -6 × -76 = (-6, -76)
  • -8 × -57 = (-8, -57)
  • -12 × -38 = (-12, -38)
  • -19 × -24 = (-19, -24)

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

Factors of 456 Solved Examples

  1. Example 1: How many factors are there for 456?

    Solution:

    The factors of 456 are too many, therefore if we can find the prime factorization of 456, 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 456 = 23 × 31 × 191
    Therefore, the total number of factors are (3 + 1) × (1 + 1) × (1 + 1) = 4 × 2 × 2 = 16

  2. Example 2: Find the LCM and Greatest Common Factor (GCF) of 456 and 297.

    Solution:

    The factors of 456 are 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456 and factors of 297 are 1, 3, 9, 11, 27, 33, 99, 297.

    Therefore, the LCM of 456 and 297 is 45144 and Greatest Common Factor (GCF) of 456 and 297 is 3.

  3. Example 3: Find if 3, 4, 8, 38, 68, 114, 228 and 456 are factors of 456.

    Solution:

    When we divide 456 by 68 it leaves a remainder. Therefore, the number 68 is not a factor of 456. All numbers except 68 are factors of 456.

  4. Example 4: Find the product of all the prime factors of 456.

    Solution:

    Since, the prime factors of 456 are 2, 3, 19. Therefore, the product of prime factors = 2 × 3 × 19 = 114.

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FAQs on Factors of 456

What are the Factors of 456?

The factors of 456 are 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456 and its negative factors are -1, -2, -3, -4, -6, -8, -12, -19, -24, -38, -57, -76, -114, -152, -228, -456.

What is the Sum of all the Factors of 456?

Sum of all factors of 456 = (23 + 1 - 1)/(2 - 1) × (31 + 1 - 1)/(3 - 1) × (191 + 1 - 1)/(19 - 1) = 1200

What are the Pair Factors of 456?

The pair factors of 456 are (1, 456), (2, 228), (3, 152), (4, 114), (6, 76), (8, 57), (12, 38), (19, 24).

What is the Greatest Common Factor of 456 and 398?

The factors of 456 and 398 are 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456 and 1, 2, 199, 398 respectively.

Common factors of 456 and 398 are [1, 2].

Hence, the GCF of 456 and 398 is 2.

How Many Factors of 456 are also common to the Factors of 144?

Since, the factors of 456 are 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456 and the factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144.
Hence, [1, 2, 3, 4, 6, 8, 12, 24] are the common factors of 456 and 144.

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