What is the Greatest Common Factor of 65954 and 65968?

Greatest common factor (GCF) of 65954 and 65968 is 14.

GCF(65954,65968) = 14

We will now calculate the prime factors of 65954 and 65968, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65954 and 65968.

How to find the GCF of 65954 and 65968?

We will first find the prime factorization of 65954 and 65968. After we will calculate the factors of 65954 and 65968 and find the biggest common factor number .

Step-1: Prime Factorization of 65954

Prime factors of 65954 are 2, 7, 673. Prime factorization of 65954 in exponential form is:

65954 = 2¹ × 7² × 673¹

Step-2: Prime Factorization of 65968

Prime factors of 65968 are 2, 7, 19, 31. Prime factorization of 65968 in exponential form is:

65968 = 2⁴ × 7¹ × 19¹ × 31¹

Step-3: Factors of 65954

List of positive integer factors of 65954 that divides 65954 without a remainder.

1, 2, 7, 14, 49, 98, 673, 1346, 4711, 9422, 32977

Step-4: Factors of 65968

List of positive integer factors of 65968 that divides 65954 without a remainder.

1, 2, 4, 7, 8, 14, 16, 19, 28, 31, 38, 56, 62, 76, 112, 124, 133, 152, 217, 248, 266, 304, 434, 496, 532, 589, 868, 1064, 1178, 1736, 2128, 2356, 3472, 4123, 4712, 8246, 9424, 16492, 32984

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65954 and 65968. The biggest common factor number is the GCF number.
So the greatest common factor 65954 and 65968 is 14.

Also check out the Least Common Multiple of 65954 and 65968