What is the Greatest Common Factor of 3400 and 3420?

Greatest common factor (GCF) of 3400 and 3420 is 20.

GCF(3400,3420) = 20

We will now calculate the prime factors of 3400 and 3420, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3400 and 3420.

How to find the GCF of 3400 and 3420?

We will first find the prime factorization of 3400 and 3420. After we will calculate the factors of 3400 and 3420 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 3420

Prime factors of 3420 are 2, 3, 5, 19. Prime factorization of 3420 in exponential form is:

3420 = 2² × 3² × 5¹ × 19¹

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 3420

List of positive integer factors of 3420 that divides 3400 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 19, 20, 30, 36, 38, 45, 57, 60, 76, 90, 95, 114, 171, 180, 190, 228, 285, 342, 380, 570, 684, 855, 1140, 1710

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3400 and 3420. The biggest common factor number is the GCF number.
So the greatest common factor 3400 and 3420 is 20.

Also check out the Least Common Multiple of 3400 and 3420