What is the Greatest Common Factor of 35300 and 35310?

Greatest common factor (GCF) of 35300 and 35310 is 10.

GCF(35300,35310) = 10

We will now calculate the prime factors of 35300 and 35310, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35300 and 35310.

How to find the GCF of 35300 and 35310?

We will first find the prime factorization of 35300 and 35310. After we will calculate the factors of 35300 and 35310 and find the biggest common factor number .

Step-1: Prime Factorization of 35300

Prime factors of 35300 are 2, 5, 353. Prime factorization of 35300 in exponential form is:

35300 = 2² × 5² × 353¹

Step-2: Prime Factorization of 35310

Prime factors of 35310 are 2, 3, 5, 11, 107. Prime factorization of 35310 in exponential form is:

35310 = 2¹ × 3¹ × 5¹ × 11¹ × 107¹

Step-3: Factors of 35300

List of positive integer factors of 35300 that divides 35300 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 353, 706, 1412, 1765, 3530, 7060, 8825, 17650

Step-4: Factors of 35310

List of positive integer factors of 35310 that divides 35300 without a remainder.

1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 107, 110, 165, 214, 321, 330, 535, 642, 1070, 1177, 1605, 2354, 3210, 3531, 5885, 7062, 11770, 17655

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35300 and 35310. The biggest common factor number is the GCF number.
So the greatest common factor 35300 and 35310 is 10.

Also check out the Least Common Multiple of 35300 and 35310