What is the Greatest Common Factor of 62400 and 62414?

Greatest common factor (GCF) of 62400 and 62414 is 2.

GCF(62400,62414) = 2

We will now calculate the prime factors of 62400 and 62414, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 62400 and 62414.

How to find the GCF of 62400 and 62414?

We will first find the prime factorization of 62400 and 62414. After we will calculate the factors of 62400 and 62414 and find the biggest common factor number .

Step-1: Prime Factorization of 62400

Prime factors of 62400 are 2, 3, 5, 13. Prime factorization of 62400 in exponential form is:

62400 = 2⁶ × 3¹ × 5² × 13¹

Step-2: Prime Factorization of 62414

Prime factors of 62414 are 2, 11, 2837. Prime factorization of 62414 in exponential form is:

62414 = 2¹ × 11¹ × 2837¹

Step-3: Factors of 62400

List of positive integer factors of 62400 that divides 62400 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 24, 25, 26, 30, 32, 39, 40, 48, 50, 52, 60, 64, 65, 75, 78, 80, 96, 100, 104, 120, 130, 150, 156, 160, 192, 195, 200, 208, 240, 260, 300, 312, 320, 325, 390, 400, 416, 480, 520, 600, 624, 650, 780, 800, 832, 960, 975, 1040, 1200, 1248, 1300, 1560, 1600, 1950, 2080, 2400, 2496, 2600, 3120, 3900, 4160, 4800, 5200, 6240, 7800, 10400, 12480, 15600, 20800, 31200

Step-4: Factors of 62414

List of positive integer factors of 62414 that divides 62400 without a remainder.

1, 2, 11, 22, 2837, 5674, 31207

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 62400 and 62414. The biggest common factor number is the GCF number.
So the greatest common factor 62400 and 62414 is 2.

Also check out the Least Common Multiple of 62400 and 62414