What is the Greatest Common Factor of 38970 and 38975?

Greatest common factor (GCF) of 38970 and 38975 is 5.

GCF(38970,38975) = 5

We will now calculate the prime factors of 38970 and 38975, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38970 and 38975.

How to find the GCF of 38970 and 38975?

We will first find the prime factorization of 38970 and 38975. After we will calculate the factors of 38970 and 38975 and find the biggest common factor number .

Step-1: Prime Factorization of 38970

Prime factors of 38970 are 2, 3, 5, 433. Prime factorization of 38970 in exponential form is:

38970 = 2¹ × 3² × 5¹ × 433¹

Step-2: Prime Factorization of 38975

Prime factors of 38975 are 5, 1559. Prime factorization of 38975 in exponential form is:

38975 = 5² × 1559¹

Step-3: Factors of 38970

List of positive integer factors of 38970 that divides 38970 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90, 433, 866, 1299, 2165, 2598, 3897, 4330, 6495, 7794, 12990, 19485

Step-4: Factors of 38975

List of positive integer factors of 38975 that divides 38970 without a remainder.

1, 5, 25, 1559, 7795

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38970 and 38975. The biggest common factor number is the GCF number.
So the greatest common factor 38970 and 38975 is 5.

Also check out the Least Common Multiple of 38970 and 38975