What is the Greatest Common Factor of 15400 and 15414?

Greatest common factor (GCF) of 15400 and 15414 is 14.

GCF(15400,15414) = 14

We will now calculate the prime factors of 15400 and 15414, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15400 and 15414.

How to find the GCF of 15400 and 15414?

We will first find the prime factorization of 15400 and 15414. After we will calculate the factors of 15400 and 15414 and find the biggest common factor number .

Step-1: Prime Factorization of 15400

Prime factors of 15400 are 2, 5, 7, 11. Prime factorization of 15400 in exponential form is:

15400 = 2³ × 5² × 7¹ × 11¹

Step-2: Prime Factorization of 15414

Prime factors of 15414 are 2, 3, 7, 367. Prime factorization of 15414 in exponential form is:

15414 = 2¹ × 3¹ × 7¹ × 367¹

Step-3: Factors of 15400

List of positive integer factors of 15400 that divides 15400 without a remainder.

1, 2, 4, 5, 7, 8, 10, 11, 14, 20, 22, 25, 28, 35, 40, 44, 50, 55, 56, 70, 77, 88, 100, 110, 140, 154, 175, 200, 220, 275, 280, 308, 350, 385, 440, 550, 616, 700, 770, 1100, 1400, 1540, 1925, 2200, 3080, 3850, 7700

Step-4: Factors of 15414

List of positive integer factors of 15414 that divides 15400 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 367, 734, 1101, 2202, 2569, 5138, 7707

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 15400 and 15414. The biggest common factor number is the GCF number.
So the greatest common factor 15400 and 15414 is 14.

Also check out the Least Common Multiple of 15400 and 15414