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Factors of 1116

Factors of 1116 are integers that can be divided evenly into 1116. There are overall 18 factors of 1116 among which 1116 is the biggest factor and its prime factors are 2, 3, 31. The Prime Factorization of 1116 is 22 × 32 × 311.

  • All Factors of 1116: 1, 2, 3, 4, 6, 9, 12, 18, 31, 36, 62, 93, 124, 186, 279, 372, 558 and 1116
  • Prime Factors of 1116: 2, 3, 31
  • Prime Factorization of 1116: 22 × 32 × 311
  • Sum of Factors of 1116: 2912
1. What Are the Factors of 1116?
2. Factors of 1116 by Prime Factorization
3. Factors of 1116 in Pairs
4. FAQs on Factors of 1116
Factors of 1116

What are Factors of 1116?

Factors of 1116 are pairs of those numbers whose products result in 1116. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1116?

To find the factors of 1116, we will have to find the list of numbers that would divide 1116 without leaving any remainder.

  • 1116/1 = 1116; therefore, 1 is a factor of 1116.
  • 1116/372 = 3; therefore, 372 is a factor of 1116.
Similarly we can find other factors. Hence, the factors of 1116 are 1, 2, 3, 4, 6, 9, 12, 18, 31, 36, 62, 93, 124, 186, 279, 372, 558, 1116.

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Factors of 1116 by Prime Factorization

The number 1116 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1116. The first step is to divide the number 1116 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 1116 ÷ 2 = 558
  • 558 ÷ 2 = 279

Further dividing 279 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 279 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 1116 can be written as 22 × 32 × 311 where 2, 3, 31 are prime.

 

Factors of 1116 in Pairs

Pair factors of 1116 are the pairs of numbers that when multiplied give the product 1116. The factors of 1116 in pairs are:

  • 1 × 1116 = (1, 1116)
  • 2 × 558 = (2, 558)
  • 3 × 372 = (3, 372)
  • 4 × 279 = (4, 279)
  • 6 × 186 = (6, 186)
  • 9 × 124 = (9, 124)
  • 12 × 93 = (12, 93)
  • 18 × 62 = (18, 62)
  • 31 × 36 = (31, 36)

Negative pair factors of 1116 are:

  • -1 × -1116 = (-1, -1116)
  • -2 × -558 = (-2, -558)
  • -3 × -372 = (-3, -372)
  • -4 × -279 = (-4, -279)
  • -6 × -186 = (-6, -186)
  • -9 × -124 = (-9, -124)
  • -12 × -93 = (-12, -93)
  • -18 × -62 = (-18, -62)
  • -31 × -36 = (-31, -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 1116 Solved Examples

  1. Example 1: How many factors are there for 1116?

    Solution:

    The factors of 1116 are too many, therefore if we can find the prime factorization of 1116, 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 1116 = 22 × 32 × 311
    Therefore, the total number of factors are (2 + 1) × (2 + 1) × (1 + 1) = 3 × 3 × 2 = 18

  2. Example 2: Find the Lowest Common Multiple (LCM) and Highest Common Factor (HCF) of 1116 and 515.

    Solution:

    The factors of 1116 are 1, 2, 3, 4, 6, 9, 12, 18, 31, 36, 62, 93, 124, 186, 279, 372, 558, 1116 and factors of 515 are 1, 5, 103, 515.

    Therefore, the Lowest Common Multiple (LCM) of 1116 and 515 is 574740 and Highest Common Factor (HCF) of 1116 and 515 is 1.

  3. Example 3: Find if 1, 3, 4, 9, 12, 18, 31 and 598 are factors of 1116.

    Solution:

    When we divide 1116 by 598 it leaves a remainder. Therefore, the number 598 is not a factor of 1116. All numbers except 598 are factors of 1116.

  4. Example 4: Find the product of all the prime factors of 1116.

    Solution:

    Since, the prime factors of 1116 are 2, 3, 31. Therefore, the product of prime factors = 2 × 3 × 31 = 186.

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FAQs on Factors of 1116

What are the Factors of 1116?

The factors of 1116 are 1, 2, 3, 4, 6, 9, 12, 18, 31, 36, 62, 93, 124, 186, 279, 372, 558, 1116 and its negative factors are -1, -2, -3, -4, -6, -9, -12, -18, -31, -36, -62, -93, -124, -186, -279, -372, -558, -1116.

What is the Sum of the Factors of 1116?

Sum of all factors of 1116 = (22 + 1 - 1)/(2 - 1) × (32 + 1 - 1)/(3 - 1) × (311 + 1 - 1)/(31 - 1) = 2912

What are the Prime Factors of 1116?

The prime factors of 1116 are 2, 3, 31.

What is the Greatest Common Factor of 1116 and 691?

The factors of 1116 are 1, 2, 3, 4, 6, 9, 12, 18, 31, 36, 62, 93, 124, 186, 279, 372, 558, 1116 and the factors of 691 are 1, 691. 1116 and 691 have only one common factor which is 1. This implies that 1116 and 691 are co-prime.

Hence, the Greatest Common Factor (GCF) of 1116 and 691 is 1.

What are the Common Factors of 1116 and 1038?

Since, the factors of 1116 are 1, 2, 3, 4, 6, 9, 12, 18, 31, 36, 62, 93, 124, 186, 279, 372, 558, 1116 and the factors of 1038 are 1, 2, 3, 6, 173, 346, 519, 1038.
Hence, [1, 2, 3, 6] are the common factors of 1116 and 1038.

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