What is the Greatest Common Factor of 74298 and 74312?

Greatest common factor (GCF) of 74298 and 74312 is 14.

GCF(74298,74312) = 14

We will now calculate the prime factors of 74298 and 74312, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74298 and 74312.

How to find the GCF of 74298 and 74312?

We will first find the prime factorization of 74298 and 74312. After we will calculate the factors of 74298 and 74312 and find the biggest common factor number .

Step-1: Prime Factorization of 74298

Prime factors of 74298 are 2, 3, 7, 29, 61. Prime factorization of 74298 in exponential form is:

74298 = 2¹ × 3¹ × 7¹ × 29¹ × 61¹

Step-2: Prime Factorization of 74312

Prime factors of 74312 are 2, 7, 1327. Prime factorization of 74312 in exponential form is:

74312 = 2³ × 7¹ × 1327¹

Step-3: Factors of 74298

List of positive integer factors of 74298 that divides 74298 without a remainder.

1, 2, 3, 6, 7, 14, 21, 29, 42, 58, 61, 87, 122, 174, 183, 203, 366, 406, 427, 609, 854, 1218, 1281, 1769, 2562, 3538, 5307, 10614, 12383, 24766, 37149

Step-4: Factors of 74312

List of positive integer factors of 74312 that divides 74298 without a remainder.

1, 2, 4, 7, 8, 14, 28, 56, 1327, 2654, 5308, 9289, 10616, 18578, 37156

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74298 and 74312. The biggest common factor number is the GCF number.
So the greatest common factor 74298 and 74312 is 14.

Also check out the Least Common Multiple of 74298 and 74312