Greatest Common Factor of 1760 and 1764

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 1760, 1764 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1760 and 1764 is 4.

GCF(1760,1764) = 4

GCF of 1760 and 1764

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

GCF of:
and

Greatest Common Factor of 1760 and 1764

GCF of 1760 and 1764 is 4

Prime Factorization of 1760


2 1760
2 880
2 440
2 220
2 110
5 55
11 11
1

Prime factors of 1760 are 2,5,11. Prime factorization of 1760 in exponential form is:

1760 = 25×51×111

Prime Factorization of 1764


2 1764
2 882
3 441
3 147
7 49
7 7
1

Prime factors of 1764 are 2,3,7. Prime factorization of 1764 in exponential form is:

1764 = 22×32×72

∴ So by taking common prime factors GCF of 1760 and 1764 is 4

Greatest Common Factor of 1760 and 1764 by matching factors method

Factors of 1760

List of positive integer factors of 1760 that divides 1760 without a remainder.

1,2,4,5,8,10,11,16,20,22,32,40,44,55,80,88,110,160,176,220,352,440,880,1760

Factors of 1764

List of positive integer factors of 1764 that divides 1764 without a remainder.

1,2,3,4,6,7,9,12,14,18,21,28,36,42,49,63,84,98,126,147,196,252,294,441,588,882,1764

Greatest Common Factor

We found the factors and prime factorization of 1760 and 1764. The biggest common factor number is the GCF number.
So the greatest common factor 1760 and 1764 is 4.

Also check out the Least Common Multiple of 1760 and 1764

Properties of GCF 1760 and 1764

(i) The GCF of 1760 and 1764 is associative

GCF of 1760 and 1764 = GCF of 1764 and 1760

Related Greatest Common Factor of 1760

Related Greatest Common Factor of 1764

Frequently Asked Questions on GCF of 1760 and 1764

1. What is the GCF of 1760 and 1764?

Answer: GCF of 1760 and 1764 is 4.

2. What are the Factors of 1760?

Answer: Factors of 1760 are 1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 32, 40, 44, 55, 80, 88, 110, 160, 176, 220, 352, 440, 880, 1760. There are 24 integers that are factors of 1760. The greatest factor of 1760 is 1760.

3. What are the Factors of 1764?

Answer: Factors of 1764 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 49, 63, 84, 98, 126, 147, 196, 252, 294, 441, 588, 882, 1764. There are 27 integers that are factors of 1764. The greatest factor of 1764 is 1764.

4. How to Find the GCF of 1760 and 1764?

Answer:

Greatest Common Factor of 1760 and 1764 = 4

Step 1: Find the prime factorization of 1760

1760 = 2 x 2 x 2 x 2 x 2 x 5 x 11

Step 2: Find the prime factorization of 1764

1764 = 2 x 2 x 3 x 3 x 7 x 7

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 1760 and 1764 is 4