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Factors of 1008

Factors of 1008 are the list of integers that we can split evenly into 1008. There are 30 factors of 1008, of which the following are its prime factors 2, 3, 7. The Prime Factorization of 1008 is 24 × 32 × 71.

  • All Factors of 1008: 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504 and 1008
  • Prime Factors of 1008: 2, 3, 7
  • Prime Factorization of 1008: 24 × 32 × 71
  • Sum of Factors of 1008: 3224
1. What Are the Factors of 1008?
2. Factors of 1008 by Prime Factorization
3. Factors of 1008 in Pairs
4. FAQs on Factors of 1008
Factors of 1008

What are Factors of 1008?

Factors of 1008 are pairs of those numbers whose products result in 1008. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1008?

To find the factors of 1008, we will have to find the list of numbers that would divide 1008 without leaving any remainder.

  • 1008/28 = 36; therefore, 28 is a factor of 1008 and 36 is also a factor of 1008.
  • 1008/16 = 63; therefore, 16 is a factor of 1008 and 63 is also a factor of 1008.
Similarly we can find other factors. Hence, the factors of 1008 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, 1008.

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Factors of 1008 by Prime Factorization

The number 1008 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1008. The first step is to divide the number 1008 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 1008 ÷ 2 = 504
  • 504 ÷ 2 = 252
  • 252 ÷ 2 = 126
  • 126 ÷ 2 = 63

Further dividing 63 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 63 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 1008 can be written as 24 × 32 × 71 where 2, 3, 7 are prime.

 

Factors of 1008 in Pairs

Pair factors of 1008 are the pairs of numbers that when multiplied give the product 1008. The factors of 1008 in pairs are:

  • 1 × 1008 = (1, 1008)
  • 2 × 504 = (2, 504)
  • 3 × 336 = (3, 336)
  • 4 × 252 = (4, 252)
  • 6 × 168 = (6, 168)
  • 7 × 144 = (7, 144)
  • 8 × 126 = (8, 126)
  • 9 × 112 = (9, 112)
  • 12 × 84 = (12, 84)
  • 14 × 72 = (14, 72)
  • 16 × 63 = (16, 63)
  • 18 × 56 = (18, 56)
  • 21 × 48 = (21, 48)
  • 24 × 42 = (24, 42)
  • 28 × 36 = (28, 36)

Negative pair factors of 1008 are:

  • -1 × -1008 = (-1, -1008)
  • -2 × -504 = (-2, -504)
  • -3 × -336 = (-3, -336)
  • -4 × -252 = (-4, -252)
  • -6 × -168 = (-6, -168)
  • -7 × -144 = (-7, -144)
  • -8 × -126 = (-8, -126)
  • -9 × -112 = (-9, -112)
  • -12 × -84 = (-12, -84)
  • -14 × -72 = (-14, -72)
  • -16 × -63 = (-16, -63)
  • -18 × -56 = (-18, -56)
  • -21 × -48 = (-21, -48)
  • -24 × -42 = (-24, -42)
  • -28 × -36 = (-28, -36)

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

Factors of 1008 Solved Examples

  1. Example 1: How many factors are there for 1008?

    Solution:

    The factors of 1008 are too many, therefore if we can find the prime factorization of 1008, 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 1008 = 24 × 32 × 71
    Therefore, the total number of factors are (4 + 1) × (2 + 1) × (1 + 1) = 5 × 3 × 2 = 30

  2. Example 2: Find the Least Common Multiple (LCM) and Highest Common Factor (HCF) of 1008 and 96.

    Solution:

    The factors of 1008 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, 1008 and factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96.

    Therefore, the Least Common Multiple (LCM) of 1008 and 96 is 2016 and Highest Common Factor (HCF) of 1008 and 96 is 48.

  3. Example 3: Find if 4, 8, 9, 14, 18, 56, 72 and 562 are factors of 1008.

    Solution:

    When we divide 1008 by 562 it leaves a remainder. Therefore, the number 562 is not a factor of 1008. All numbers except 562 are factors of 1008.

  4. Example 4: Find the product of all the prime factors of 1008.

    Solution:

    Since, the prime factors of 1008 are 2, 3, 7. Therefore, the product of prime factors = 2 × 3 × 7 = 42.

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FAQs on Factors of 1008

What are the Factors of 1008?

The factors of 1008 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, 1008 and its negative factors are -1, -2, -3, -4, -6, -7, -8, -9, -12, -14, -16, -18, -21, -24, -28, -36, -42, -48, -56, -63, -72, -84, -112, -126, -144, -168, -252, -336, -504, -1008.

What is the Sum of Factors of 1008?

Sum of all factors of 1008 = (24 + 1 - 1)/(2 - 1) × (32 + 1 - 1)/(3 - 1) × (71 + 1 - 1)/(7 - 1) = 3224

What numbers are the Pair Factors of 1008?

The pair factors of 1008 are (1, 1008), (2, 504), (3, 336), (4, 252), (6, 168), (7, 144), (8, 126), (9, 112), (12, 84), (14, 72), (16, 63), (18, 56), (21, 48), (24, 42), (28, 36).

What is the Greatest Common Factor of 1008 and 853?

The factors of 1008 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, 1008 and the factors of 853 are 1, 853. 1008 and 853 have only one common factor which is 1. This implies that 1008 and 853 are co-prime.

Hence, the Greatest Common Factor (GCF) of 1008 and 853 is 1.

How Many Factors of 1008 are also Factors of 881?

Since, the factors of 1008 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, 1008 and factors of 881 are 1, 881. Hence, 1008 and 881 have only one common factor which is 1. Therefore, 1008 and 881 are co-prime.

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