Greatest Common Factor of 1696 and 1700

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 1696, 1700 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1696 and 1700 is 4.

GCF(1696,1700) = 4

GCF of 1696 and 1700

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

GCF of:
and

Greatest Common Factor of 1696 and 1700

GCF of 1696 and 1700 is 4

Prime Factorization of 1696


2 1696
2 848
2 424
2 212
2 106
53 53
1

Prime factors of 1696 are 2,53. Prime factorization of 1696 in exponential form is:

1696 = 25×531

Prime Factorization of 1700


2 1700
2 850
5 425
5 85
17 17
1

Prime factors of 1700 are 2,5,17. Prime factorization of 1700 in exponential form is:

1700 = 22×52×171

∴ So by taking common prime factors GCF of 1696 and 1700 is 4

Greatest Common Factor of 1696 and 1700 by matching factors method

Factors of 1696

List of positive integer factors of 1696 that divides 1696 without a remainder.

1,2,4,8,16,32,53,106,212,424,848,1696

Factors of 1700

List of positive integer factors of 1700 that divides 1700 without a remainder.

1,2,4,5,10,17,20,25,34,50,68,85,100,170,340,425,850,1700

Greatest Common Factor

We found the factors and prime factorization of 1696 and 1700. The biggest common factor number is the GCF number.
So the greatest common factor 1696 and 1700 is 4.

Also check out the Least Common Multiple of 1696 and 1700

Properties of GCF 1696 and 1700

(i) The GCF of 1696 and 1700 is associative

GCF of 1696 and 1700 = GCF of 1700 and 1696

Related Greatest Common Factor of 1696

Related Greatest Common Factor of 1700

Frequently Asked Questions on GCF of 1696 and 1700

1. What is the GCF of 1696 and 1700?

Answer: GCF of 1696 and 1700 is 4.

2. What are the Factors of 1696?

Answer: Factors of 1696 are 1, 2, 4, 8, 16, 32, 53, 106, 212, 424, 848, 1696. There are 12 integers that are factors of 1696. The greatest factor of 1696 is 1696.

3. What are the Factors of 1700?

Answer: Factors of 1700 are 1, 2, 4, 5, 10, 17, 20, 25, 34, 50, 68, 85, 100, 170, 340, 425, 850, 1700. There are 18 integers that are factors of 1700. The greatest factor of 1700 is 1700.

4. How to Find the GCF of 1696 and 1700?

Answer:

Greatest Common Factor of 1696 and 1700 = 4

Step 1: Find the prime factorization of 1696

1696 = 2 x 2 x 2 x 2 x 2 x 53

Step 2: Find the prime factorization of 1700

1700 = 2 x 2 x 5 x 5 x 17

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

GCF = 2 x 2 = 4

Step 4: Therefore, the greatest common factor of 1696 and 1700 is 4