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Factors of 1122

Factors of 1122 are numbers that, when multiplied in pairs give the product as 1122. There are 16 factors of 1122 of which 1122 itself is the biggest factor and its prime factors are 2, 3, 11, 17 The sum of all factors of 1122 is 2592.

  • All Factors of 1122: 1, 2, 3, 6, 11, 17, 22, 33, 34, 51, 66, 102, 187, 374, 561 and 1122
  • Prime Factors of 1122: 2, 3, 11, 17
  • Prime Factorization of 1122: 21 × 31 × 111 × 171
  • Sum of Factors of 1122: 2592
1. What Are the Factors of 1122?
2. Factors of 1122 by Prime Factorization
3. Factors of 1122 in Pairs
4. FAQs on Factors of 1122
Factors of 1122

What are Factors of 1122?

Factors of 1122 are pairs of those numbers whose products result in 1122. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1122?

To find the factors of 1122, we will have to find the list of numbers that would divide 1122 without leaving any remainder.

  • 1122/11 = 102; therefore, 11 is a factor of 1122 and 102 is also a factor of 1122.
  • 1122/51 = 22; therefore, 51 is a factor of 1122 and 22 is also a factor of 1122.
Similarly we can find other factors. Hence, the factors of 1122 are 1, 2, 3, 6, 11, 17, 22, 33, 34, 51, 66, 102, 187, 374, 561, 1122.

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Factors of 1122 by Prime Factorization

The number 1122 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1122. The first step is to divide the number 1122 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 1122 ÷ 2 = 561

Further dividing 561 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 561 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 1122 can be written as 21 × 31 × 111 × 171 where 2, 3, 11, 17 are prime.

 

Factors of 1122 in Pairs

Pair factors of 1122 are the pairs of numbers that when multiplied give the product 1122. The factors of 1122 in pairs are:

  • 1 × 1122 = (1, 1122)
  • 2 × 561 = (2, 561)
  • 3 × 374 = (3, 374)
  • 6 × 187 = (6, 187)
  • 11 × 102 = (11, 102)
  • 17 × 66 = (17, 66)
  • 22 × 51 = (22, 51)
  • 33 × 34 = (33, 34)

Negative pair factors of 1122 are:

  • -1 × -1122 = (-1, -1122)
  • -2 × -561 = (-2, -561)
  • -3 × -374 = (-3, -374)
  • -6 × -187 = (-6, -187)
  • -11 × -102 = (-11, -102)
  • -17 × -66 = (-17, -66)
  • -22 × -51 = (-22, -51)
  • -33 × -34 = (-33, -34)

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

Factors of 1122 Solved Examples

  1. Example 1: How many factors are there for 1122?

    Solution:

    The factors of 1122 are too many, therefore if we can find the prime factorization of 1122, 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 1122 = 21 × 31 × 111 × 171
    Therefore, the total number of factors are (1 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 2 × 2 × 2 × 2 = 16

  2. Example 2: Find the Lowest Common Multiple (LCM) and Highest Common Factor (HCF) of 1122 and 88.

    Solution:

    The factors of 1122 are 1, 2, 3, 6, 11, 17, 22, 33, 34, 51, 66, 102, 187, 374, 561, 1122 and factors of 88 are 1, 2, 4, 8, 11, 22, 44, 88.

    Therefore, the Lowest Common Multiple (LCM) of 1122 and 88 is 4488 and Highest Common Factor (HCF) of 1122 and 88 is 22.

  3. Example 3: Find if 1, 2, 17, 34, 51, 374, 465 and 561 are factors of 1122.

    Solution:

    When we divide 1122 by 465 it leaves a remainder. Therefore, the number 465 is not a factor of 1122. All numbers except 465 are factors of 1122.

  4. Example 4: Find the product of all the prime factors of 1122.

    Solution:

    Since, the prime factors of 1122 are 2, 3, 11, 17. Therefore, the product of prime factors = 2 × 3 × 11 × 17 = 1122.

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FAQs on Factors of 1122

What are the Factors of 1122?

The factors of 1122 are 1, 2, 3, 6, 11, 17, 22, 33, 34, 51, 66, 102, 187, 374, 561, 1122 and its negative factors are -1, -2, -3, -6, -11, -17, -22, -33, -34, -51, -66, -102, -187, -374, -561, -1122.

What is the Sum of Factors of 1122?

Sum of all factors of 1122 = (21 + 1 - 1)/(2 - 1) × (31 + 1 - 1)/(3 - 1) × (111 + 1 - 1)/(11 - 1) × (171 + 1 - 1)/(17 - 1) = 2592

What Numbers are the Prime Factors of 1122?

The prime factors of 1122 are 2, 3, 11, 17.

What is the Greatest Common Factor of 1122 and 597?

The factors of 1122 and 597 are 1, 2, 3, 6, 11, 17, 22, 33, 34, 51, 66, 102, 187, 374, 561, 1122 and 1, 3, 199, 597 respectively.

Common factors of 1122 and 597 are [1, 3].

Hence, the Greatest Common Factor (GCF) of 1122 and 597 is 3.

How Many Factors of 1122 are also Factors of 113?

Since, the factors of 1122 are 1, 2, 3, 6, 11, 17, 22, 33, 34, 51, 66, 102, 187, 374, 561, 1122 and factors of 113 are 1, 113. Hence, 1122 and 113 have only one common factor which is 1. Therefore, 1122 and 113 are co-prime.

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