What is the Greatest Common Factor of 34700 and 34710?

Greatest common factor (GCF) of 34700 and 34710 is 10.

GCF(34700,34710) = 10

We will now calculate the prime factors of 34700 and 34710, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34700 and 34710.

How to find the GCF of 34700 and 34710?

We will first find the prime factorization of 34700 and 34710. After we will calculate the factors of 34700 and 34710 and find the biggest common factor number .

Step-1: Prime Factorization of 34700

Prime factors of 34700 are 2, 5, 347. Prime factorization of 34700 in exponential form is:

34700 = 2² × 5² × 347¹

Step-2: Prime Factorization of 34710

Prime factors of 34710 are 2, 3, 5, 13, 89. Prime factorization of 34710 in exponential form is:

34710 = 2¹ × 3¹ × 5¹ × 13¹ × 89¹

Step-3: Factors of 34700

List of positive integer factors of 34700 that divides 34700 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 347, 694, 1388, 1735, 3470, 6940, 8675, 17350

Step-4: Factors of 34710

List of positive integer factors of 34710 that divides 34700 without a remainder.

1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 89, 130, 178, 195, 267, 390, 445, 534, 890, 1157, 1335, 2314, 2670, 3471, 5785, 6942, 11570, 17355

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34700 and 34710. The biggest common factor number is the GCF number.
So the greatest common factor 34700 and 34710 is 10.

Also check out the Least Common Multiple of 34700 and 34710