What is the Greatest Common Factor of 1760 and 1772?

Greatest common factor (GCF) of 1760 and 1772 is 4.

GCF(1760,1772) = 4

We will now calculate the prime factors of 1760 and 1772, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1760 and 1772.

How to find the GCF of 1760 and 1772?

We will first find the prime factorization of 1760 and 1772. After we will calculate the factors of 1760 and 1772 and find the biggest common factor number .

Step-1: Prime Factorization of 1760

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

1760 = 2⁵ × 5¹ × 11¹

Step-2: Prime Factorization of 1772

Prime factors of 1772 are 2, 443. Prime factorization of 1772 in exponential form is:

1772 = 2² × 443¹

Step-3: 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

Step-4: Factors of 1772

List of positive integer factors of 1772 that divides 1760 without a remainder.

1, 2, 4, 443, 886

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1760 and 1772. The biggest common factor number is the GCF number.
So the greatest common factor 1760 and 1772 is 4.

Also check out the Least Common Multiple of 1760 and 1772