What is the Greatest Common Factor of 61760 and 61770?

Greatest common factor (GCF) of 61760 and 61770 is 10.

GCF(61760,61770) = 10

We will now calculate the prime factors of 61760 and 61770, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 61760 and 61770.

How to find the GCF of 61760 and 61770?

We will first find the prime factorization of 61760 and 61770. After we will calculate the factors of 61760 and 61770 and find the biggest common factor number .

Step-1: Prime Factorization of 61760

Prime factors of 61760 are 2, 5, 193. Prime factorization of 61760 in exponential form is:

61760 = 2⁶ × 5¹ × 193¹

Step-2: Prime Factorization of 61770

Prime factors of 61770 are 2, 3, 5, 29, 71. Prime factorization of 61770 in exponential form is:

61770 = 2¹ × 3¹ × 5¹ × 29¹ × 71¹

Step-3: Factors of 61760

List of positive integer factors of 61760 that divides 61760 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 193, 320, 386, 772, 965, 1544, 1930, 3088, 3860, 6176, 7720, 12352, 15440, 30880

Step-4: Factors of 61770

List of positive integer factors of 61770 that divides 61760 without a remainder.

1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 71, 87, 142, 145, 174, 213, 290, 355, 426, 435, 710, 870, 1065, 2059, 2130, 4118, 6177, 10295, 12354, 20590, 30885

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 61760 and 61770. The biggest common factor number is the GCF number.
So the greatest common factor 61760 and 61770 is 10.

Also check out the Least Common Multiple of 61760 and 61770