What is the Greatest Common Factor of 61680 and 61700?

Greatest common factor (GCF) of 61680 and 61700 is 20.

GCF(61680,61700) = 20

We will now calculate the prime factors of 61680 and 61700, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 61680 and 61700.

How to find the GCF of 61680 and 61700?

We will first find the prime factorization of 61680 and 61700. After we will calculate the factors of 61680 and 61700 and find the biggest common factor number .

Step-1: Prime Factorization of 61680

Prime factors of 61680 are 2, 3, 5, 257. Prime factorization of 61680 in exponential form is:

61680 = 2⁴ × 3¹ × 5¹ × 257¹

Step-2: Prime Factorization of 61700

Prime factors of 61700 are 2, 5, 617. Prime factorization of 61700 in exponential form is:

61700 = 2² × 5² × 617¹

Step-3: Factors of 61680

List of positive integer factors of 61680 that divides 61680 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240, 257, 514, 771, 1028, 1285, 1542, 2056, 2570, 3084, 3855, 4112, 5140, 6168, 7710, 10280, 12336, 15420, 20560, 30840

Step-4: Factors of 61700

List of positive integer factors of 61700 that divides 61680 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 617, 1234, 2468, 3085, 6170, 12340, 15425, 30850

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 61680 and 61700. The biggest common factor number is the GCF number.
So the greatest common factor 61680 and 61700 is 20.

Also check out the Least Common Multiple of 61680 and 61700