What is the Greatest Common Factor of 52400 and 52416?

Greatest common factor (GCF) of 52400 and 52416 is 16.

GCF(52400,52416) = 16

We will now calculate the prime factors of 52400 and 52416, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 52400 and 52416.

How to find the GCF of 52400 and 52416?

We will first find the prime factorization of 52400 and 52416. After we will calculate the factors of 52400 and 52416 and find the biggest common factor number .

Step-1: Prime Factorization of 52400

Prime factors of 52400 are 2, 5, 131. Prime factorization of 52400 in exponential form is:

52400 = 2⁴ × 5² × 131¹

Step-2: Prime Factorization of 52416

Prime factors of 52416 are 2, 3, 7, 13. Prime factorization of 52416 in exponential form is:

52416 = 2⁶ × 3² × 7¹ × 13¹

Step-3: Factors of 52400

List of positive integer factors of 52400 that divides 52400 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 131, 200, 262, 400, 524, 655, 1048, 1310, 2096, 2620, 3275, 5240, 6550, 10480, 13100, 26200

Step-4: Factors of 52416

List of positive integer factors of 52416 that divides 52400 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 16, 18, 21, 24, 26, 28, 32, 36, 39, 42, 48, 52, 56, 63, 64, 72, 78, 84, 91, 96, 104, 112, 117, 126, 144, 156, 168, 182, 192, 208, 224, 234, 252, 273, 288, 312, 336, 364, 416, 448, 468, 504, 546, 576, 624, 672, 728, 819, 832, 936, 1008, 1092, 1248, 1344, 1456, 1638, 1872, 2016, 2184, 2496, 2912, 3276, 3744, 4032, 4368, 5824, 6552, 7488, 8736, 13104, 17472, 26208

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 52400 and 52416. The biggest common factor number is the GCF number.
So the greatest common factor 52400 and 52416 is 16.

Also check out the Least Common Multiple of 52400 and 52416