What is the Greatest Common Factor of 69400 and 69408?

Greatest common factor (GCF) of 69400 and 69408 is 8.

GCF(69400,69408) = 8

We will now calculate the prime factors of 69400 and 69408, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69400 and 69408.

How to find the GCF of 69400 and 69408?

We will first find the prime factorization of 69400 and 69408. After we will calculate the factors of 69400 and 69408 and find the biggest common factor number .

Step-1: Prime Factorization of 69400

Prime factors of 69400 are 2, 5, 347. Prime factorization of 69400 in exponential form is:

69400 = 2³ × 5² × 347¹

Step-2: Prime Factorization of 69408

Prime factors of 69408 are 2, 3, 241. Prime factorization of 69408 in exponential form is:

69408 = 2⁵ × 3² × 241¹

Step-3: Factors of 69400

List of positive integer factors of 69400 that divides 69400 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200, 347, 694, 1388, 1735, 2776, 3470, 6940, 8675, 13880, 17350, 34700

Step-4: Factors of 69408

List of positive integer factors of 69408 that divides 69400 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 241, 288, 482, 723, 964, 1446, 1928, 2169, 2892, 3856, 4338, 5784, 7712, 8676, 11568, 17352, 23136, 34704

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69400 and 69408. The biggest common factor number is the GCF number.
So the greatest common factor 69400 and 69408 is 8.

Also check out the Least Common Multiple of 69400 and 69408