What is the Greatest Common Factor of 74900 and 74914?

Greatest common factor (GCF) of 74900 and 74914 is 14.

GCF(74900,74914) = 14

We will now calculate the prime factors of 74900 and 74914, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74900 and 74914.

How to find the GCF of 74900 and 74914?

We will first find the prime factorization of 74900 and 74914. After we will calculate the factors of 74900 and 74914 and find the biggest common factor number .

Step-1: Prime Factorization of 74900

Prime factors of 74900 are 2, 5, 7, 107. Prime factorization of 74900 in exponential form is:

74900 = 2² × 5² × 7¹ × 107¹

Step-2: Prime Factorization of 74914

Prime factors of 74914 are 2, 7, 5351. Prime factorization of 74914 in exponential form is:

74914 = 2¹ × 7¹ × 5351¹

Step-3: Factors of 74900

List of positive integer factors of 74900 that divides 74900 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 107, 140, 175, 214, 350, 428, 535, 700, 749, 1070, 1498, 2140, 2675, 2996, 3745, 5350, 7490, 10700, 14980, 18725, 37450

Step-4: Factors of 74914

List of positive integer factors of 74914 that divides 74900 without a remainder.

1, 2, 7, 14, 5351, 10702, 37457

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74900 and 74914. The biggest common factor number is the GCF number.
So the greatest common factor 74900 and 74914 is 14.

Also check out the Least Common Multiple of 74900 and 74914