What is the Greatest Common Factor of 67952 and 67970?

Greatest common factor (GCF) of 67952 and 67970 is 2.

GCF(67952,67970) = 2

We will now calculate the prime factors of 67952 and 67970, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67952 and 67970.

How to find the GCF of 67952 and 67970?

We will first find the prime factorization of 67952 and 67970. After we will calculate the factors of 67952 and 67970 and find the biggest common factor number .

Step-1: Prime Factorization of 67952

Prime factors of 67952 are 2, 31, 137. Prime factorization of 67952 in exponential form is:

67952 = 2⁴ × 31¹ × 137¹

Step-2: Prime Factorization of 67970

Prime factors of 67970 are 2, 5, 7, 971. Prime factorization of 67970 in exponential form is:

67970 = 2¹ × 5¹ × 7¹ × 971¹

Step-3: Factors of 67952

List of positive integer factors of 67952 that divides 67952 without a remainder.

1, 2, 4, 8, 16, 31, 62, 124, 137, 248, 274, 496, 548, 1096, 2192, 4247, 8494, 16988, 33976

Step-4: Factors of 67970

List of positive integer factors of 67970 that divides 67952 without a remainder.

1, 2, 5, 7, 10, 14, 35, 70, 971, 1942, 4855, 6797, 9710, 13594, 33985

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67952 and 67970. The biggest common factor number is the GCF number.
So the greatest common factor 67952 and 67970 is 2.

Also check out the Least Common Multiple of 67952 and 67970