What is the Greatest Common Factor of 71400 and 71414?

Greatest common factor (GCF) of 71400 and 71414 is 14.

GCF(71400,71414) = 14

We will now calculate the prime factors of 71400 and 71414, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71400 and 71414.

How to find the GCF of 71400 and 71414?

We will first find the prime factorization of 71400 and 71414. After we will calculate the factors of 71400 and 71414 and find the biggest common factor number .

Step-1: Prime Factorization of 71400

Prime factors of 71400 are 2, 3, 5, 7, 17. Prime factorization of 71400 in exponential form is:

71400 = 2³ × 3¹ × 5² × 7¹ × 17¹

Step-2: Prime Factorization of 71414

Prime factors of 71414 are 2, 7, 5101. Prime factorization of 71414 in exponential form is:

71414 = 2¹ × 7¹ × 5101¹

Step-3: Factors of 71400

List of positive integer factors of 71400 that divides 71400 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 17, 20, 21, 24, 25, 28, 30, 34, 35, 40, 42, 50, 51, 56, 60, 68, 70, 75, 84, 85, 100, 102, 105, 119, 120, 136, 140, 150, 168, 170, 175, 200, 204, 210, 238, 255, 280, 300, 340, 350, 357, 408, 420, 425, 476, 510, 525, 595, 600, 680, 700, 714, 840, 850, 952, 1020, 1050, 1190, 1275, 1400, 1428, 1700, 1785, 2040, 2100, 2380, 2550, 2856, 2975, 3400, 3570, 4200, 4760, 5100, 5950, 7140, 8925, 10200, 11900, 14280, 17850, 23800, 35700

Step-4: Factors of 71414

List of positive integer factors of 71414 that divides 71400 without a remainder.

1, 2, 7, 14, 5101, 10202, 35707

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 71400 and 71414. The biggest common factor number is the GCF number.
So the greatest common factor 71400 and 71414 is 14.

Also check out the Least Common Multiple of 71400 and 71414