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Factors of 1664

Factors of 1664 are the list of integers that we can split evenly into 1664. There are total 16 factors of 1664, of which 2, 13 are its prime factors. The sum of all factors of 1664 is 3570.

  • All Factors of 1664: 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832 and 1664
  • Prime Factors of 1664: 2, 13
  • Prime Factorization of 1664: 27 × 131
  • Sum of Factors of 1664: 3570
1. What Are the Factors of 1664?
2. Factors of 1664 by Prime Factorization
3. Factors of 1664 in Pairs
4. FAQs on Factors of 1664
Factors of 1664

What are Factors of 1664?

Factors of 1664 are pairs of those numbers whose products result in 1664. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1664?

To find the factors of 1664, we will have to find the list of numbers that would divide 1664 without leaving any remainder.

  • 1664/32 = 52; therefore, 32 is a factor of 1664 and 52 is also a factor of 1664.
  • 1664/4 = 416; therefore, 4 is a factor of 1664 and 416 is also a factor of 1664.
Similarly we can find other factors. Hence, the factors of 1664 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, 1664.

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Factors of 1664 by Prime Factorization

The number 1664 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1664. The first step is to divide the number 1664 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 1664 ÷ 2 = 832
  • 832 ÷ 2 = 416
  • 416 ÷ 2 = 208
  • 208 ÷ 2 = 104
  • 104 ÷ 2 = 52
  • 52 ÷ 2 = 26
  • 26 ÷ 2 = 13

Further dividing 13 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 13 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 1664 can be written as 27 × 131 where 2, 13 are prime.

 

Factors of 1664 in Pairs

Pair factors of 1664 are the pairs of numbers that when multiplied give the product 1664. The factors of 1664 in pairs are:

  • 1 × 1664 = (1, 1664)
  • 2 × 832 = (2, 832)
  • 4 × 416 = (4, 416)
  • 8 × 208 = (8, 208)
  • 13 × 128 = (13, 128)
  • 16 × 104 = (16, 104)
  • 26 × 64 = (26, 64)
  • 32 × 52 = (32, 52)

Negative pair factors of 1664 are:

  • -1 × -1664 = (-1, -1664)
  • -2 × -832 = (-2, -832)
  • -4 × -416 = (-4, -416)
  • -8 × -208 = (-8, -208)
  • -13 × -128 = (-13, -128)
  • -16 × -104 = (-16, -104)
  • -26 × -64 = (-26, -64)
  • -32 × -52 = (-32, -52)

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

Factors of 1664 Solved Examples

  1. Example 1: How many factors are there for 1664?

    Solution:

    The factors of 1664 are too many, therefore if we can find the prime factorization of 1664, 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 1664 = 27 × 131
    Therefore, the total number of factors are (7 + 1) × (1 + 1) = 8 × 2 = 16

  2. Example 2: Find the Least Common Multiple and Greatest Common Factor (GCF) of 1664 and 562.

    Solution:

    The factors of 1664 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, 1664 and factors of 562 are 1, 2, 281, 562.

    Therefore, the Least Common Multiple of 1664 and 562 is 467584 and Greatest Common Factor (GCF) of 1664 and 562 is 2.

  3. Example 3: Find if 8, 13, 32, 64, 208, 379, 416 and 832 are factors of 1664.

    Solution:

    When we divide 1664 by 379 it leaves a remainder. Therefore, the number 379 is not a factor of 1664. All numbers except 379 are factors of 1664.

  4. Example 4: Find the product of all the prime factors of 1664.

    Solution:

    Since, the prime factors of 1664 are 2, 13. Therefore, the product of prime factors = 2 × 13 = 26.

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FAQs on Factors of 1664

What are the Factors of 1664?

The factors of 1664 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, 1664 and its negative factors are -1, -2, -4, -8, -13, -16, -26, -32, -52, -64, -104, -128, -208, -416, -832, -1664.

What is the Sum of Factors of 1664?

Sum of all factors of 1664 = (27 + 1 - 1)/(2 - 1) × (131 + 1 - 1)/(13 - 1) = 3570

What are Pair Factors of 1664?

The pair factors of 1664 are (1, 1664), (2, 832), (4, 416), (8, 208), (13, 128), (16, 104), (26, 64), (32, 52).

What is the Greatest Common Factor of 1664 and 1401?

The factors of 1664 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, 1664 and the factors of 1401 are 1, 3, 467, 1401. 1664 and 1401 have only one common factor which is 1. This implies that 1664 and 1401 are co-prime.

Hence, the Greatest Common Factor (GCF) of 1664 and 1401 is 1.

What are the Common Factors of 1664 and 832?

Since, the factors of 1664 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, 1664 and the factors of 832 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 208, 416, 832.
Hence, [1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 208, 416, 832] are the common factors of 1664 and 832.

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