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Factors of 1144

Factors of 1144 are integers that can be divided evenly into 1144. There are 16 factors of 1144 of which 1144 itself is the biggest factor and its prime factors are 2, 11, 13 The sum of all factors of 1144 is 2520.

  • All Factors of 1144: 1, 2, 4, 8, 11, 13, 22, 26, 44, 52, 88, 104, 143, 286, 572 and 1144
  • Prime Factors of 1144: 2, 11, 13
  • Prime Factorization of 1144: 23 × 111 × 131
  • Sum of Factors of 1144: 2520
1. What Are the Factors of 1144?
2. Factors of 1144 by Prime Factorization
3. Factors of 1144 in Pairs
4. FAQs on Factors of 1144
Factors of 1144

What are Factors of 1144?

Factors of 1144 are pairs of those numbers whose products result in 1144. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1144?

To find the factors of 1144, we will have to find the list of numbers that would divide 1144 without leaving any remainder.

  • 1144/26 = 44; therefore, 26 is a factor of 1144 and 44 is also a factor of 1144.
  • 1144/572 = 2; therefore, 572 is a factor of 1144 and 2 is also a factor of 1144.
Similarly we can find other factors. Hence, the factors of 1144 are 1, 2, 4, 8, 11, 13, 22, 26, 44, 52, 88, 104, 143, 286, 572, 1144.

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Factors of 1144 by Prime Factorization

The number 1144 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1144. The first step is to divide the number 1144 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 1144 ÷ 2 = 572
  • 572 ÷ 2 = 286
  • 286 ÷ 2 = 143

Further dividing 143 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 143 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 1144 can be written as 23 × 111 × 131 where 2, 11, 13 are prime.

 

Factors of 1144 in Pairs

Pair factors of 1144 are the pairs of numbers that when multiplied give the product 1144. The factors of 1144 in pairs are:

  • 1 × 1144 = (1, 1144)
  • 2 × 572 = (2, 572)
  • 4 × 286 = (4, 286)
  • 8 × 143 = (8, 143)
  • 11 × 104 = (11, 104)
  • 13 × 88 = (13, 88)
  • 22 × 52 = (22, 52)
  • 26 × 44 = (26, 44)

Negative pair factors of 1144 are:

  • -1 × -1144 = (-1, -1144)
  • -2 × -572 = (-2, -572)
  • -4 × -286 = (-4, -286)
  • -8 × -143 = (-8, -143)
  • -11 × -104 = (-11, -104)
  • -13 × -88 = (-13, -88)
  • -22 × -52 = (-22, -52)
  • -26 × -44 = (-26, -44)

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

Factors of 1144 Solved Examples

  1. Example 1: How many factors are there for 1144?

    Solution:

    The factors of 1144 are too many, therefore if we can find the prime factorization of 1144, 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 1144 = 23 × 111 × 131
    Therefore, the total number of factors are (3 + 1) × (1 + 1) × (1 + 1) = 4 × 2 × 2 = 16

  2. Example 2: Find the Least Common Multiple (LCM) and Greatest Common Divisor (GCD) of 1144 and 1015.

    Solution:

    The factors of 1144 are 1, 2, 4, 8, 11, 13, 22, 26, 44, 52, 88, 104, 143, 286, 572, 1144 and factors of 1015 are 1, 5, 7, 29, 35, 145, 203, 1015.

    Therefore, the Least Common Multiple (LCM) of 1144 and 1015 is 1161160 and Greatest Common Divisor (GCD) of 1144 and 1015 is 1.

  3. Example 3: Find if 1, 8, 13, 22, 44, 104, 143 and 882 are factors of 1144.

    Solution:

    When we divide 1144 by 882 it leaves a remainder. Therefore, the number 882 is not a factor of 1144. All numbers except 882 are factors of 1144.

  4. Example 4: Find the product of all the prime factors of 1144.

    Solution:

    Since, the prime factors of 1144 are 2, 11, 13. Therefore, the product of prime factors = 2 × 11 × 13 = 286.

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FAQs on Factors of 1144

What are the Factors of 1144?

The factors of 1144 are 1, 2, 4, 8, 11, 13, 22, 26, 44, 52, 88, 104, 143, 286, 572, 1144 and its negative factors are -1, -2, -4, -8, -11, -13, -22, -26, -44, -52, -88, -104, -143, -286, -572, -1144.

What is the Sum of all Factors of 1144?

Sum of all factors of 1144 = (23 + 1 - 1)/(2 - 1) × (111 + 1 - 1)/(11 - 1) × (131 + 1 - 1)/(13 - 1) = 2520

What are Pair Factors of 1144?

The pair factors of 1144 are (1, 1144), (2, 572), (4, 286), (8, 143), (11, 104), (13, 88), (22, 52), (26, 44).

What is the Greatest Common Factor of 1144 and 785?

The factors of 1144 are 1, 2, 4, 8, 11, 13, 22, 26, 44, 52, 88, 104, 143, 286, 572, 1144 and the factors of 785 are 1, 5, 157, 785. 1144 and 785 have only one common factor which is 1. This implies that 1144 and 785 are co-prime.

Hence, the Greatest Common Factor (GCF) of 1144 and 785 is 1.

How Many Factors of 1144 are also Factors of 1143?

Since, the factors of 1144 are 1, 2, 4, 8, 11, 13, 22, 26, 44, 52, 88, 104, 143, 286, 572, 1144 and factors of 1143 are 1, 3, 9, 127, 381, 1143. Hence, 1144 and 1143 have only one common factor which is 1. Therefore, 1144 and 1143 are co-prime.

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