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Factors of 1092

Factors of 1092 are integers that can be divided evenly into 1092. There are overall 24 factors of 1092, of which 2, 3, 7, 13 are its prime factors. The sum of all factors of 1092 is 3136.

  • All Factors of 1092: 1, 2, 3, 4, 6, 7, 12, 13, 14, 21, 26, 28, 39, 42, 52, 78, 84, 91, 156, 182, 273, 364, 546 and 1092
  • Prime Factors of 1092: 2, 3, 7, 13
  • Prime Factorization of 1092: 22 × 31 × 71 × 131
  • Sum of Factors of 1092: 3136
1. What Are the Factors of 1092?
2. Factors of 1092 by Prime Factorization
3. Factors of 1092 in Pairs
4. FAQs on Factors of 1092
Factors of 1092

What are Factors of 1092?

Factors of 1092 are pairs of those numbers whose products result in 1092. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1092?

To find the factors of 1092, we will have to find the list of numbers that would divide 1092 without leaving any remainder.

  • 1092/26 = 42; therefore, 26 is a factor of 1092 and 42 is also a factor of 1092.
  • 1092/78 = 14; therefore, 78 is a factor of 1092 and 14 is also a factor of 1092.
Similarly we can find other factors. Hence, the factors of 1092 are 1, 2, 3, 4, 6, 7, 12, 13, 14, 21, 26, 28, 39, 42, 52, 78, 84, 91, 156, 182, 273, 364, 546, 1092.

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Factors of 1092 by Prime Factorization

The number 1092 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1092. The first step is to divide the number 1092 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 1092 ÷ 2 = 546
  • 546 ÷ 2 = 273

Further dividing 273 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 273 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 1092 can be written as 22 × 31 × 71 × 131 where 2, 3, 7, 13 are prime.

 

Factors of 1092 in Pairs

Pair factors of 1092 are the pairs of numbers that when multiplied give the product 1092. The factors of 1092 in pairs are:

  • 1 × 1092 = (1, 1092)
  • 2 × 546 = (2, 546)
  • 3 × 364 = (3, 364)
  • 4 × 273 = (4, 273)
  • 6 × 182 = (6, 182)
  • 7 × 156 = (7, 156)
  • 12 × 91 = (12, 91)
  • 13 × 84 = (13, 84)
  • 14 × 78 = (14, 78)
  • 21 × 52 = (21, 52)
  • 26 × 42 = (26, 42)
  • 28 × 39 = (28, 39)

Negative pair factors of 1092 are:

  • -1 × -1092 = (-1, -1092)
  • -2 × -546 = (-2, -546)
  • -3 × -364 = (-3, -364)
  • -4 × -273 = (-4, -273)
  • -6 × -182 = (-6, -182)
  • -7 × -156 = (-7, -156)
  • -12 × -91 = (-12, -91)
  • -13 × -84 = (-13, -84)
  • -14 × -78 = (-14, -78)
  • -21 × -52 = (-21, -52)
  • -26 × -42 = (-26, -42)
  • -28 × -39 = (-28, -39)

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

Factors of 1092 Solved Examples

  1. Example 1: How many factors are there for 1092?

    Solution:

    The factors of 1092 are too many, therefore if we can find the prime factorization of 1092, 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 1092 = 22 × 31 × 71 × 131
    Therefore, the total number of factors are (2 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 3 × 2 × 2 × 2 = 24

  2. Example 2: Find the LCM and Greatest Common Divisor (GCD) of 1092 and 632.

    Solution:

    The factors of 1092 are 1, 2, 3, 4, 6, 7, 12, 13, 14, 21, 26, 28, 39, 42, 52, 78, 84, 91, 156, 182, 273, 364, 546, 1092 and factors of 632 are 1, 2, 4, 8, 79, 158, 316, 632.

    Therefore, the LCM of 1092 and 632 is 172536 and Greatest Common Divisor (GCD) of 1092 and 632 is 4.

  3. Example 3: Find if 2, 13, 52, 84, 91, 546, 787 and 1092 are factors of 1092.

    Solution:

    When we divide 1092 by 787 it leaves a remainder. Therefore, the number 787 is not a factor of 1092. All numbers except 787 are factors of 1092.

  4. Example 4: Find the product of all the prime factors of 1092.

    Solution:

    Since, the prime factors of 1092 are 2, 3, 7, 13. Therefore, the product of prime factors = 2 × 3 × 7 × 13 = 546.

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FAQs on Factors of 1092

What are the Factors of 1092?

The factors of 1092 are 1, 2, 3, 4, 6, 7, 12, 13, 14, 21, 26, 28, 39, 42, 52, 78, 84, 91, 156, 182, 273, 364, 546, 1092 and its negative factors are -1, -2, -3, -4, -6, -7, -12, -13, -14, -21, -26, -28, -39, -42, -52, -78, -84, -91, -156, -182, -273, -364, -546, -1092.

What is the Sum of all Factors of 1092?

Sum of all factors of 1092 = (22 + 1 - 1)/(2 - 1) × (31 + 1 - 1)/(3 - 1) × (71 + 1 - 1)/(7 - 1) × (131 + 1 - 1)/(13 - 1) = 3136

What Numbers are the Prime Factors of 1092?

The prime factors of 1092 are 2, 3, 7, 13.

What is the Greatest Common Factor of 1092 and 407?

The factors of 1092 are 1, 2, 3, 4, 6, 7, 12, 13, 14, 21, 26, 28, 39, 42, 52, 78, 84, 91, 156, 182, 273, 364, 546, 1092 and the factors of 407 are 1, 11, 37, 407. 1092 and 407 have only one common factor which is 1. This implies that 1092 and 407 are co-prime.

Hence, the Greatest Common Factor (GCF) of 1092 and 407 is 1.

What are the Common Factors of 1092 and 54?

Since, the factors of 1092 are 1, 2, 3, 4, 6, 7, 12, 13, 14, 21, 26, 28, 39, 42, 52, 78, 84, 91, 156, 182, 273, 364, 546, 1092 and the factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54.
Hence, [1, 2, 3, 6] are the common factors of 1092 and 54.

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