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Factors of 1056

Factors of 1056 are numbers that, when multiplied in pairs give the product as 1056. There are overall 24 factors of 1056 among which 1056 is the biggest factor and 2, 3, 11 are its prime factors. The sum of all factors of 1056 is 3024.

  • All Factors of 1056: 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 32, 33, 44, 48, 66, 88, 96, 132, 176, 264, 352, 528 and 1056
  • Prime Factors of 1056: 2, 3, 11
  • Prime Factorization of 1056: 25 × 31 × 111
  • Sum of Factors of 1056: 3024
1. What Are the Factors of 1056?
2. Factors of 1056 by Prime Factorization
3. Factors of 1056 in Pairs
4. FAQs on Factors of 1056
Factors of 1056

What are Factors of 1056?

Factors of 1056 are pairs of those numbers whose products result in 1056. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1056?

To find the factors of 1056, we will have to find the list of numbers that would divide 1056 without leaving any remainder.

  • 1056/96 = 11; therefore, 96 is a factor of 1056 and 11 is also a factor of 1056.
  • 1056/176 = 6; therefore, 176 is a factor of 1056 and 6 is also a factor of 1056.
Similarly we can find other factors. Hence, the factors of 1056 are 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 32, 33, 44, 48, 66, 88, 96, 132, 176, 264, 352, 528, 1056.

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Factors of 1056 by Prime Factorization

The number 1056 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1056. The first step is to divide the number 1056 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 1056 ÷ 2 = 528
  • 528 ÷ 2 = 264
  • 264 ÷ 2 = 132
  • 132 ÷ 2 = 66
  • 66 ÷ 2 = 33

Further dividing 33 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 33 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 1056 can be written as 25 × 31 × 111 where 2, 3, 11 are prime.

 

Factors of 1056 in Pairs

Pair factors of 1056 are the pairs of numbers that when multiplied give the product 1056. The factors of 1056 in pairs are:

  • 1 × 1056 = (1, 1056)
  • 2 × 528 = (2, 528)
  • 3 × 352 = (3, 352)
  • 4 × 264 = (4, 264)
  • 6 × 176 = (6, 176)
  • 8 × 132 = (8, 132)
  • 11 × 96 = (11, 96)
  • 12 × 88 = (12, 88)
  • 16 × 66 = (16, 66)
  • 22 × 48 = (22, 48)
  • 24 × 44 = (24, 44)
  • 32 × 33 = (32, 33)

Negative pair factors of 1056 are:

  • -1 × -1056 = (-1, -1056)
  • -2 × -528 = (-2, -528)
  • -3 × -352 = (-3, -352)
  • -4 × -264 = (-4, -264)
  • -6 × -176 = (-6, -176)
  • -8 × -132 = (-8, -132)
  • -11 × -96 = (-11, -96)
  • -12 × -88 = (-12, -88)
  • -16 × -66 = (-16, -66)
  • -22 × -48 = (-22, -48)
  • -24 × -44 = (-24, -44)
  • -32 × -33 = (-32, -33)

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

Factors of 1056 Solved Examples

  1. Example 1: How many factors are there for 1056?

    Solution:

    The factors of 1056 are too many, therefore if we can find the prime factorization of 1056, 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 1056 = 25 × 31 × 111
    Therefore, the total number of factors are (5 + 1) × (1 + 1) × (1 + 1) = 6 × 2 × 2 = 24

  2. Example 2: Find the Least Common Multiple (LCM) and Greatest Common Factor (GCF) of 1056 and 829.

    Solution:

    The factors of 1056 are 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 32, 33, 44, 48, 66, 88, 96, 132, 176, 264, 352, 528, 1056 and factors of 829 are 1, 829.

    Therefore, the Least Common Multiple (LCM) of 1056 and 829 is 875424 and Greatest Common Factor (GCF) of 1056 and 829 is 1.

  3. Example 3: Find if 1, 3, 12, 16, 24, 257, 264 and 1056 are factors of 1056.

    Solution:

    When we divide 1056 by 257 it leaves a remainder. Therefore, the number 257 is not a factor of 1056. All numbers except 257 are factors of 1056.

  4. Example 4: Find the product of all the prime factors of 1056.

    Solution:

    Since, the prime factors of 1056 are 2, 3, 11. Therefore, the product of prime factors = 2 × 3 × 11 = 66.

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FAQs on Factors of 1056

What are the Factors of 1056?

The factors of 1056 are 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 32, 33, 44, 48, 66, 88, 96, 132, 176, 264, 352, 528, 1056 and its negative factors are -1, -2, -3, -4, -6, -8, -11, -12, -16, -22, -24, -32, -33, -44, -48, -66, -88, -96, -132, -176, -264, -352, -528, -1056.

What is the Sum of Factors of 1056?

Sum of all factors of 1056 = (25 + 1 - 1)/(2 - 1) × (31 + 1 - 1)/(3 - 1) × (111 + 1 - 1)/(11 - 1) = 3024

What Numbers are the Prime Factors of 1056?

The prime factors of 1056 are 2, 3, 11.

What is the Greatest Common Factor of 1056 and 134?

The factors of 1056 and 134 are 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 32, 33, 44, 48, 66, 88, 96, 132, 176, 264, 352, 528, 1056 and 1, 2, 67, 134 respectively.

Common factors of 1056 and 134 are [1, 2].

Hence, the Greatest Common Factor (GCF) of 1056 and 134 is 2.

How Many Factors of 1056 are also Factors of 987?

Since, the factors of 1056 are 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 32, 33, 44, 48, 66, 88, 96, 132, 176, 264, 352, 528, 1056 and the factors of 987 are 1, 3, 7, 21, 47, 141, 329, 987.
Hence, [1, 3] are the common factors of 1056 and 987.

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