What is the Greatest Common Factor of 53946 and 53960?

Greatest common factor (GCF) of 53946 and 53960 is 2.

GCF(53946,53960) = 2

We will now calculate the prime factors of 53946 and 53960, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 53946 and 53960.

How to find the GCF of 53946 and 53960?

We will first find the prime factorization of 53946 and 53960. After we will calculate the factors of 53946 and 53960 and find the biggest common factor number .

Step-1: Prime Factorization of 53946

Prime factors of 53946 are 2, 3, 37. Prime factorization of 53946 in exponential form is:

53946 = 2¹ × 3⁶ × 37¹

Step-2: Prime Factorization of 53960

Prime factors of 53960 are 2, 5, 19, 71. Prime factorization of 53960 in exponential form is:

53960 = 2³ × 5¹ × 19¹ × 71¹

Step-3: Factors of 53946

List of positive integer factors of 53946 that divides 53946 without a remainder.

1, 2, 3, 6, 9, 18, 27, 37, 54, 74, 81, 111, 162, 222, 243, 333, 486, 666, 729, 999, 1458, 1998, 2997, 5994, 8991, 17982, 26973

Step-4: Factors of 53960

List of positive integer factors of 53960 that divides 53946 without a remainder.

1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 71, 76, 95, 142, 152, 190, 284, 355, 380, 568, 710, 760, 1349, 1420, 2698, 2840, 5396, 6745, 10792, 13490, 26980

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 53946 and 53960. The biggest common factor number is the GCF number.
So the greatest common factor 53946 and 53960 is 2.

Also check out the Least Common Multiple of 53946 and 53960