What is the Greatest Common Factor of 61745 and 61760?

Greatest common factor (GCF) of 61745 and 61760 is 5.

GCF(61745,61760) = 5

We will now calculate the prime factors of 61745 and 61760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 61745 and 61760.

How to find the GCF of 61745 and 61760?

We will first find the prime factorization of 61745 and 61760. After we will calculate the factors of 61745 and 61760 and find the biggest common factor number .

Step-1: Prime Factorization of 61745

Prime factors of 61745 are 5, 53, 233. Prime factorization of 61745 in exponential form is:

61745 = 5¹ × 53¹ × 233¹

Step-2: 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-3: Factors of 61745

List of positive integer factors of 61745 that divides 61745 without a remainder.

1, 5, 53, 233, 265, 1165, 12349

Step-4: Factors of 61760

List of positive integer factors of 61760 that divides 61745 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 61745 and 61760. The biggest common factor number is the GCF number.
So the greatest common factor 61745 and 61760 is 5.

Also check out the Least Common Multiple of 61745 and 61760