What is the Greatest Common Factor of 35204 and 35210?

Greatest common factor (GCF) of 35204 and 35210 is 2.

GCF(35204,35210) = 2

We will now calculate the prime factors of 35204 and 35210, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35204 and 35210.

How to find the GCF of 35204 and 35210?

We will first find the prime factorization of 35204 and 35210. After we will calculate the factors of 35204 and 35210 and find the biggest common factor number .

Step-1: Prime Factorization of 35204

Prime factors of 35204 are 2, 13, 677. Prime factorization of 35204 in exponential form is:

35204 = 2² × 13¹ × 677¹

Step-2: Prime Factorization of 35210

Prime factors of 35210 are 2, 5, 7, 503. Prime factorization of 35210 in exponential form is:

35210 = 2¹ × 5¹ × 7¹ × 503¹

Step-3: Factors of 35204

List of positive integer factors of 35204 that divides 35204 without a remainder.

1, 2, 4, 13, 26, 52, 677, 1354, 2708, 8801, 17602

Step-4: Factors of 35210

List of positive integer factors of 35210 that divides 35204 without a remainder.

1, 2, 5, 7, 10, 14, 35, 70, 503, 1006, 2515, 3521, 5030, 7042, 17605

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35204 and 35210. The biggest common factor number is the GCF number.
So the greatest common factor 35204 and 35210 is 2.

Also check out the Least Common Multiple of 35204 and 35210