What is the Greatest Common Factor of 53400 and 53414?

Greatest common factor (GCF) of 53400 and 53414 is 2.

GCF(53400,53414) = 2

We will now calculate the prime factors of 53400 and 53414, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 53400 and 53414.

How to find the GCF of 53400 and 53414?

We will first find the prime factorization of 53400 and 53414. After we will calculate the factors of 53400 and 53414 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 53414

Prime factors of 53414 are 2, 17, 1571. Prime factorization of 53414 in exponential form is:

53414 = 2¹ × 17¹ × 1571¹

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 53414

List of positive integer factors of 53414 that divides 53400 without a remainder.

1, 2, 17, 34, 1571, 3142, 26707

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 53400 and 53414. The biggest common factor number is the GCF number.
So the greatest common factor 53400 and 53414 is 2.

Also check out the Least Common Multiple of 53400 and 53414