Greatest Common Factor of 1656 and 1664

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023


Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 1656, 1664 i.e. 8 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1656 and 1664 is 8.

GCF(1656,1664) = 8

GCF of 1656 and 1664

Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;

GCF of:
and

Greatest Common Factor of 1656 and 1664

GCF of 1656 and 1664 is 8

Prime Factorization of 1656


2 1656
2 828
2 414
3 207
3 69
23 23
1

Prime factors of 1656 are 2,3,23. Prime factorization of 1656 in exponential form is:

1656 = 23×32×231

Prime Factorization of 1664


2 1664
2 832
2 416
2 208
2 104
2 52
2 26
13 13
1

Prime factors of 1664 are 2,13. Prime factorization of 1664 in exponential form is:

1664 = 27×131

∴ So by taking common prime factors GCF of 1656 and 1664 is 8

Greatest Common Factor of 1656 and 1664 by matching factors method

Factors of 1656

List of positive integer factors of 1656 that divides 1656 without a remainder.

1,2,3,4,6,8,9,12,18,23,24,36,46,69,72,92,138,184,207,276,414,552,828,1656

Factors of 1664

List of positive integer factors of 1664 that divides 1664 without a remainder.

1,2,4,8,13,16,26,32,52,64,104,128,208,416,832,1664

Greatest Common Factor

We found the factors and prime factorization of 1656 and 1664. The biggest common factor number is the GCF number.
So the greatest common factor 1656 and 1664 is 8.

Also check out the Least Common Multiple of 1656 and 1664

Properties of GCF 1656 and 1664

(i) The GCF of 1656 and 1664 is associative

GCF of 1656 and 1664 = GCF of 1664 and 1656

Frequently Asked Questions on GCF of 1656 and 1664

1. What is the GCF of 1656 and 1664?

Answer: GCF of 1656 and 1664 is 8.

2. What are the Factors of 1656?

Answer: Factors of 1656 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 23, 24, 36, 46, 69, 72, 92, 138, 184, 207, 276, 414, 552, 828, 1656. There are 24 integers that are factors of 1656. The greatest factor of 1656 is 1656.

3. What are the Factors of 1664?

Answer: Factors of 1664 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, 1664. There are 16 integers that are factors of 1664. The greatest factor of 1664 is 1664.

4. How to Find the GCF of 1656 and 1664?

Answer:

Greatest Common Factor of 1656 and 1664 = 8

Step 1: Find the prime factorization of 1656

1656 = 2 x 2 x 2 x 3 x 3 x 23

Step 2: Find the prime factorization of 1664

1664 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 13

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 2 x 2 x 2 = 8

Step 4: Therefore, the greatest common factor of 1656 and 1664 is 8