What is the Greatest Common Factor of 73984 and 74001?

Greatest common factor (GCF) of 73984 and 74001 is 17.

GCF(73984,74001) = 17

We will now calculate the prime factors of 73984 and 74001, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 73984 and 74001.

How to find the GCF of 73984 and 74001?

We will first find the prime factorization of 73984 and 74001. After we will calculate the factors of 73984 and 74001 and find the biggest common factor number .

Step-1: Prime Factorization of 73984

Prime factors of 73984 are 2, 17. Prime factorization of 73984 in exponential form is:

73984 = 2⁸ × 17²

Step-2: Prime Factorization of 74001

Prime factors of 74001 are 3, 17, 1451. Prime factorization of 74001 in exponential form is:

74001 = 3¹ × 17¹ × 1451¹

Step-3: Factors of 73984

List of positive integer factors of 73984 that divides 73984 without a remainder.

1, 2, 4, 8, 16, 17, 32, 34, 64, 68, 128, 136, 256, 272, 289, 544, 578, 1088, 1156, 2176, 2312, 4352, 4624, 9248, 18496, 36992

Step-4: Factors of 74001

List of positive integer factors of 74001 that divides 73984 without a remainder.

1, 3, 17, 51, 1451, 4353, 24667

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 73984 and 74001. The biggest common factor number is the GCF number.
So the greatest common factor 73984 and 74001 is 17.

Also check out the Least Common Multiple of 73984 and 74001