What is the Greatest Common Factor of 74086 and 74100?

Greatest common factor (GCF) of 74086 and 74100 is 2.

GCF(74086,74100) = 2

We will now calculate the prime factors of 74086 and 74100, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74086 and 74100.

How to find the GCF of 74086 and 74100?

We will first find the prime factorization of 74086 and 74100. After we will calculate the factors of 74086 and 74100 and find the biggest common factor number .

Step-1: Prime Factorization of 74086

Prime factors of 74086 are 2, 17, 2179. Prime factorization of 74086 in exponential form is:

74086 = 2¹ × 17¹ × 2179¹

Step-2: Prime Factorization of 74100

Prime factors of 74100 are 2, 3, 5, 13, 19. Prime factorization of 74100 in exponential form is:

74100 = 2² × 3¹ × 5² × 13¹ × 19¹

Step-3: Factors of 74086

List of positive integer factors of 74086 that divides 74086 without a remainder.

1, 2, 17, 34, 2179, 4358, 37043

Step-4: Factors of 74100

List of positive integer factors of 74100 that divides 74086 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 19, 20, 25, 26, 30, 38, 39, 50, 52, 57, 60, 65, 75, 76, 78, 95, 100, 114, 130, 150, 156, 190, 195, 228, 247, 260, 285, 300, 325, 380, 390, 475, 494, 570, 650, 741, 780, 950, 975, 988, 1140, 1235, 1300, 1425, 1482, 1900, 1950, 2470, 2850, 2964, 3705, 3900, 4940, 5700, 6175, 7410, 12350, 14820, 18525, 24700, 37050

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74086 and 74100. The biggest common factor number is the GCF number.
So the greatest common factor 74086 and 74100 is 2.

Also check out the Least Common Multiple of 74086 and 74100