What is the Greatest Common Factor of 39700 and 39705?

Greatest common factor (GCF) of 39700 and 39705 is 5.

GCF(39700,39705) = 5

We will now calculate the prime factors of 39700 and 39705, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39700 and 39705.

How to find the GCF of 39700 and 39705?

We will first find the prime factorization of 39700 and 39705. After we will calculate the factors of 39700 and 39705 and find the biggest common factor number .

Step-1: Prime Factorization of 39700

Prime factors of 39700 are 2, 5, 397. Prime factorization of 39700 in exponential form is:

39700 = 2² × 5² × 397¹

Step-2: Prime Factorization of 39705

Prime factors of 39705 are 3, 5, 2647. Prime factorization of 39705 in exponential form is:

39705 = 3¹ × 5¹ × 2647¹

Step-3: Factors of 39700

List of positive integer factors of 39700 that divides 39700 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 397, 794, 1588, 1985, 3970, 7940, 9925, 19850

Step-4: Factors of 39705

List of positive integer factors of 39705 that divides 39700 without a remainder.

1, 3, 5, 15, 2647, 7941, 13235

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39700 and 39705. The biggest common factor number is the GCF number.
So the greatest common factor 39700 and 39705 is 5.

Also check out the Least Common Multiple of 39700 and 39705