What is the Greatest Common Factor of 53400 and 53408?

Greatest common factor (GCF) of 53400 and 53408 is 8.

GCF(53400,53408) = 8

We will now calculate the prime factors of 53400 and 53408, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 53400 and 53408.

How to find the GCF of 53400 and 53408?

We will first find the prime factorization of 53400 and 53408. After we will calculate the factors of 53400 and 53408 and find the biggest common factor number .

Step-1: Prime Factorization of 53400

Prime factors of 53400 are 2, 3, 5, 89. Prime factorization of 53400 in exponential form is:

53400 = 2³ × 3¹ × 5² × 89¹

Step-2: Prime Factorization of 53408

Prime factors of 53408 are 2, 1669. Prime factorization of 53408 in exponential form is:

53408 = 2⁵ × 1669¹

Step-3: Factors of 53400

List of positive integer factors of 53400 that divides 53400 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 89, 100, 120, 150, 178, 200, 267, 300, 356, 445, 534, 600, 712, 890, 1068, 1335, 1780, 2136, 2225, 2670, 3560, 4450, 5340, 6675, 8900, 10680, 13350, 17800, 26700

Step-4: Factors of 53408

List of positive integer factors of 53408 that divides 53400 without a remainder.

1, 2, 4, 8, 16, 32, 1669, 3338, 6676, 13352, 26704

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 53400 and 53408. The biggest common factor number is the GCF number.
So the greatest common factor 53400 and 53408 is 8.

Also check out the Least Common Multiple of 53400 and 53408