What is the Greatest Common Factor of 75970 and 75980?

Greatest common factor (GCF) of 75970 and 75980 is 10.

GCF(75970,75980) = 10

We will now calculate the prime factors of 75970 and 75980, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75970 and 75980.

How to find the GCF of 75970 and 75980?

We will first find the prime factorization of 75970 and 75980. After we will calculate the factors of 75970 and 75980 and find the biggest common factor number .

Step-1: Prime Factorization of 75970

Prime factors of 75970 are 2, 5, 71, 107. Prime factorization of 75970 in exponential form is:

75970 = 2¹ × 5¹ × 71¹ × 107¹

Step-2: Prime Factorization of 75980

Prime factors of 75980 are 2, 5, 29, 131. Prime factorization of 75980 in exponential form is:

75980 = 2² × 5¹ × 29¹ × 131¹

Step-3: Factors of 75970

List of positive integer factors of 75970 that divides 75970 without a remainder.

1, 2, 5, 10, 71, 107, 142, 214, 355, 535, 710, 1070, 7597, 15194, 37985

Step-4: Factors of 75980

List of positive integer factors of 75980 that divides 75970 without a remainder.

1, 2, 4, 5, 10, 20, 29, 58, 116, 131, 145, 262, 290, 524, 580, 655, 1310, 2620, 3799, 7598, 15196, 18995, 37990

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75970 and 75980. The biggest common factor number is the GCF number.
So the greatest common factor 75970 and 75980 is 10.

Also check out the Least Common Multiple of 75970 and 75980