What is the Greatest Common Factor of 55314 and 55320?

Greatest common factor (GCF) of 55314 and 55320 is 6.

GCF(55314,55320) = 6

We will now calculate the prime factors of 55314 and 55320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 55314 and 55320.

How to find the GCF of 55314 and 55320?

We will first find the prime factorization of 55314 and 55320. After we will calculate the factors of 55314 and 55320 and find the biggest common factor number .

Step-1: Prime Factorization of 55314

Prime factors of 55314 are 2, 3, 7, 439. Prime factorization of 55314 in exponential form is:

55314 = 2¹ × 3² × 7¹ × 439¹

Step-2: Prime Factorization of 55320

Prime factors of 55320 are 2, 3, 5, 461. Prime factorization of 55320 in exponential form is:

55320 = 2³ × 3¹ × 5¹ × 461¹

Step-3: Factors of 55314

List of positive integer factors of 55314 that divides 55314 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126, 439, 878, 1317, 2634, 3073, 3951, 6146, 7902, 9219, 18438, 27657

Step-4: Factors of 55320

List of positive integer factors of 55320 that divides 55314 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, 461, 922, 1383, 1844, 2305, 2766, 3688, 4610, 5532, 6915, 9220, 11064, 13830, 18440, 27660

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 55314 and 55320. The biggest common factor number is the GCF number.
So the greatest common factor 55314 and 55320 is 6.

Also check out the Least Common Multiple of 55314 and 55320