What is the Greatest Common Factor of 3400 and 3410?

Greatest common factor (GCF) of 3400 and 3410 is 10.

GCF(3400,3410) = 10

We will now calculate the prime factors of 3400 and 3410, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3400 and 3410.

How to find the GCF of 3400 and 3410?

We will first find the prime factorization of 3400 and 3410. After we will calculate the factors of 3400 and 3410 and find the biggest common factor number .

Step-1: Prime Factorization of 3400

Prime factors of 3400 are 2, 5, 17. Prime factorization of 3400 in exponential form is:

3400 = 2³ × 5² × 17¹

Step-2: Prime Factorization of 3410

Prime factors of 3410 are 2, 5, 11, 31. Prime factorization of 3410 in exponential form is:

3410 = 2¹ × 5¹ × 11¹ × 31¹

Step-3: Factors of 3400

List of positive integer factors of 3400 that divides 3400 without a remainder.

1, 2, 4, 5, 8, 10, 17, 20, 25, 34, 40, 50, 68, 85, 100, 136, 170, 200, 340, 425, 680, 850, 1700

Step-4: Factors of 3410

List of positive integer factors of 3410 that divides 3400 without a remainder.

1, 2, 5, 10, 11, 22, 31, 55, 62, 110, 155, 310, 341, 682, 1705

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3400 and 3410. The biggest common factor number is the GCF number.
So the greatest common factor 3400 and 3410 is 10.

Also check out the Least Common Multiple of 3400 and 3410