What is the Greatest Common Factor of 34074 and 34080?

Greatest common factor (GCF) of 34074 and 34080 is 6.

GCF(34074,34080) = 6

We will now calculate the prime factors of 34074 and 34080, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34074 and 34080.

How to find the GCF of 34074 and 34080?

We will first find the prime factorization of 34074 and 34080. After we will calculate the factors of 34074 and 34080 and find the biggest common factor number .

Step-1: Prime Factorization of 34074

Prime factors of 34074 are 2, 3, 631. Prime factorization of 34074 in exponential form is:

34074 = 2¹ × 3³ × 631¹

Step-2: Prime Factorization of 34080

Prime factors of 34080 are 2, 3, 5, 71. Prime factorization of 34080 in exponential form is:

34080 = 2⁵ × 3¹ × 5¹ × 71¹

Step-3: Factors of 34074

List of positive integer factors of 34074 that divides 34074 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 631, 1262, 1893, 3786, 5679, 11358, 17037

Step-4: Factors of 34080

List of positive integer factors of 34080 that divides 34074 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 71, 80, 96, 120, 142, 160, 213, 240, 284, 355, 426, 480, 568, 710, 852, 1065, 1136, 1420, 1704, 2130, 2272, 2840, 3408, 4260, 5680, 6816, 8520, 11360, 17040

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34074 and 34080. The biggest common factor number is the GCF number.
So the greatest common factor 34074 and 34080 is 6.

Also check out the Least Common Multiple of 34074 and 34080