What is the Greatest Common Factor of 61314 and 61320?

Greatest common factor (GCF) of 61314 and 61320 is 6.

GCF(61314,61320) = 6

We will now calculate the prime factors of 61314 and 61320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 61314 and 61320.

How to find the GCF of 61314 and 61320?

We will first find the prime factorization of 61314 and 61320. After we will calculate the factors of 61314 and 61320 and find the biggest common factor number .

Step-1: Prime Factorization of 61314

Prime factors of 61314 are 2, 3, 11, 929. Prime factorization of 61314 in exponential form is:

61314 = 2¹ × 3¹ × 11¹ × 929¹

Step-2: Prime Factorization of 61320

Prime factors of 61320 are 2, 3, 5, 7, 73. Prime factorization of 61320 in exponential form is:

61320 = 2³ × 3¹ × 5¹ × 7¹ × 73¹

Step-3: Factors of 61314

List of positive integer factors of 61314 that divides 61314 without a remainder.

1, 2, 3, 6, 11, 22, 33, 66, 929, 1858, 2787, 5574, 10219, 20438, 30657

Step-4: Factors of 61320

List of positive integer factors of 61320 that divides 61314 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 73, 84, 105, 120, 140, 146, 168, 210, 219, 280, 292, 365, 420, 438, 511, 584, 730, 840, 876, 1022, 1095, 1460, 1533, 1752, 2044, 2190, 2555, 2920, 3066, 4088, 4380, 5110, 6132, 7665, 8760, 10220, 12264, 15330, 20440, 30660

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 61314 and 61320. The biggest common factor number is the GCF number.
So the greatest common factor 61314 and 61320 is 6.

Also check out the Least Common Multiple of 61314 and 61320