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Factors of 2744

Factors of 2744 are the list of integers that we can split evenly into 2744. There are total 16 factors of 2744, of which 2, 7 are its prime factors. The sum of all factors of 2744 is 6000.

  • All Factors of 2744: 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 343, 392, 686, 1372 and 2744
  • Prime Factors of 2744: 2, 7
  • Prime Factorization of 2744: 23 × 73
  • Sum of Factors of 2744: 6000
1. What Are the Factors of 2744?
2. Factors of 2744 by Prime Factorization
3. Factors of 2744 in Pairs
4. FAQs on Factors of 2744
Factors of 2744

What are Factors of 2744?

Factors of 2744 are pairs of those numbers whose products result in 2744. These factors are either prime numbers or composite numbers.

How to Find the Factors of 2744?

To find the factors of 2744, we will have to find the list of numbers that would divide 2744 without leaving any remainder.

  • 2744/7 = 392; therefore, 7 is a factor of 2744 and 392 is also a factor of 2744.
  • 2744/8 = 343; therefore, 8 is a factor of 2744 and 343 is also a factor of 2744.
Similarly we can find other factors. Hence, the factors of 2744 are 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 343, 392, 686, 1372, 2744.

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Factors of 2744 by Prime Factorization

The number 2744 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 2744. The first step is to divide the number 2744 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 2744 ÷ 2 = 1372
  • 1372 ÷ 2 = 686
  • 686 ÷ 2 = 343

Further dividing 343 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 343 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 2744 can be written as 23 × 73 where 2, 7 are prime.

 

Factors of 2744 in Pairs

Pair factors of 2744 are the pairs of numbers that when multiplied give the product 2744. The factors of 2744 in pairs are:

  • 1 × 2744 = (1, 2744)
  • 2 × 1372 = (2, 1372)
  • 4 × 686 = (4, 686)
  • 7 × 392 = (7, 392)
  • 8 × 343 = (8, 343)
  • 14 × 196 = (14, 196)
  • 28 × 98 = (28, 98)
  • 49 × 56 = (49, 56)

Negative pair factors of 2744 are:

  • -1 × -2744 = (-1, -2744)
  • -2 × -1372 = (-2, -1372)
  • -4 × -686 = (-4, -686)
  • -7 × -392 = (-7, -392)
  • -8 × -343 = (-8, -343)
  • -14 × -196 = (-14, -196)
  • -28 × -98 = (-28, -98)
  • -49 × -56 = (-49, -56)

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

Factors of 2744 Solved Examples

  1. Example 1: How many factors are there for 2744?

    Solution:

    The factors of 2744 are too many, therefore if we can find the prime factorization of 2744, 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 2744 = 23 × 73
    Therefore, the total number of factors are (3 + 1) × (3 + 1) = 4 × 4 = 16

  2. Example 2: Find the Least Common Multiple (LCM) and Highest Common Factor (HCF) of 2744 and 346.

    Solution:

    The factors of 2744 are 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 343, 392, 686, 1372, 2744 and factors of 346 are 1, 2, 173, 346.

    Therefore, the Least Common Multiple (LCM) of 2744 and 346 is 474712 and Highest Common Factor (HCF) of 2744 and 346 is 2.

  3. Example 3: Find if 8, 14, 28, 49, 56, 130, 343 and 392 are factors of 2744.

    Solution:

    When we divide 2744 by 130 it leaves a remainder. Therefore, the number 130 is not a factor of 2744. All numbers except 130 are factors of 2744.

  4. Example 4: Find the product of all the prime factors of 2744.

    Solution:

    Since, the prime factors of 2744 are 2, 7. Therefore, the product of prime factors = 2 × 7 = 14.

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FAQs on Factors of 2744

What are the Factors of 2744?

The factors of 2744 are 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 343, 392, 686, 1372, 2744 and its negative factors are -1, -2, -4, -7, -8, -14, -28, -49, -56, -98, -196, -343, -392, -686, -1372, -2744.

What is the Sum of Factors of 2744?

Sum of all factors of 2744 = (23 + 1 - 1)/(2 - 1) × (73 + 1 - 1)/(7 - 1) = 6000

What are the Prime Factors of 2744?

The prime factors of 2744 are 2, 7.

What is the Greatest Common Factor of 2744 and 936?

The factors of 2744 and 936 are 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 343, 392, 686, 1372, 2744 and 1, 2, 3, 4, 6, 8, 9, 12, 13, 18, 24, 26, 36, 39, 52, 72, 78, 104, 117, 156, 234, 312, 468, 936 respectively.

Common factors of 2744 and 936 are [1, 2, 4, 8].

Hence, the Greatest Common Factor of 2744 and 936 is 8.

How Many Factors of 2559 are also common to the Factors of 2744?

Since, the factors of 2744 are 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 343, 392, 686, 1372, 2744 and factors of 2559 are 1, 3, 853, 2559. Hence, 2744 and 2559 have only one common factor which is 1. Therefore, 2744 and 2559 are co-prime.

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