What is the Greatest Common Factor of 34400 and 34416?

Greatest common factor (GCF) of 34400 and 34416 is 16.

GCF(34400,34416) = 16

We will now calculate the prime factors of 34400 and 34416, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34400 and 34416.

How to find the GCF of 34400 and 34416?

We will first find the prime factorization of 34400 and 34416. After we will calculate the factors of 34400 and 34416 and find the biggest common factor number .

Step-1: Prime Factorization of 34400

Prime factors of 34400 are 2, 5, 43. Prime factorization of 34400 in exponential form is:

34400 = 2⁵ × 5² × 43¹

Step-2: Prime Factorization of 34416

Prime factors of 34416 are 2, 3, 239. Prime factorization of 34416 in exponential form is:

34416 = 2⁴ × 3² × 239¹

Step-3: Factors of 34400

List of positive integer factors of 34400 that divides 34400 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 43, 50, 80, 86, 100, 160, 172, 200, 215, 344, 400, 430, 688, 800, 860, 1075, 1376, 1720, 2150, 3440, 4300, 6880, 8600, 17200

Step-4: Factors of 34416

List of positive integer factors of 34416 that divides 34400 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 239, 478, 717, 956, 1434, 1912, 2151, 2868, 3824, 4302, 5736, 8604, 11472, 17208

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34400 and 34416. The biggest common factor number is the GCF number.
So the greatest common factor 34400 and 34416 is 16.

Also check out the Least Common Multiple of 34400 and 34416