What is the Greatest Common Factor of 61600 and 61610?

Greatest common factor (GCF) of 61600 and 61610 is 10.

GCF(61600,61610) = 10

We will now calculate the prime factors of 61600 and 61610, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 61600 and 61610.

How to find the GCF of 61600 and 61610?

We will first find the prime factorization of 61600 and 61610. After we will calculate the factors of 61600 and 61610 and find the biggest common factor number .

Step-1: Prime Factorization of 61600

Prime factors of 61600 are 2, 5, 7, 11. Prime factorization of 61600 in exponential form is:

61600 = 2⁵ × 5² × 7¹ × 11¹

Step-2: Prime Factorization of 61610

Prime factors of 61610 are 2, 5, 61, 101. Prime factorization of 61610 in exponential form is:

61610 = 2¹ × 5¹ × 61¹ × 101¹

Step-3: Factors of 61600

List of positive integer factors of 61600 that divides 61600 without a remainder.

1, 2, 4, 5, 7, 8, 10, 11, 14, 16, 20, 22, 25, 28, 32, 35, 40, 44, 50, 55, 56, 70, 77, 80, 88, 100, 110, 112, 140, 154, 160, 175, 176, 200, 220, 224, 275, 280, 308, 350, 352, 385, 400, 440, 550, 560, 616, 700, 770, 800, 880, 1100, 1120, 1232, 1400, 1540, 1760, 1925, 2200, 2464, 2800, 3080, 3850, 4400, 5600, 6160, 7700, 8800, 12320, 15400, 30800

Step-4: Factors of 61610

List of positive integer factors of 61610 that divides 61600 without a remainder.

1, 2, 5, 10, 61, 101, 122, 202, 305, 505, 610, 1010, 6161, 12322, 30805

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 61600 and 61610. The biggest common factor number is the GCF number.
So the greatest common factor 61600 and 61610 is 10.

Also check out the Least Common Multiple of 61600 and 61610