What is the Greatest Common Factor of 15408 and 15414?

Greatest common factor (GCF) of 15408 and 15414 is 6.

GCF(15408,15414) = 6

We will now calculate the prime factors of 15408 and 15414, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15408 and 15414.

How to find the GCF of 15408 and 15414?

We will first find the prime factorization of 15408 and 15414. After we will calculate the factors of 15408 and 15414 and find the biggest common factor number .

Step-1: Prime Factorization of 15408

Prime factors of 15408 are 2, 3, 107. Prime factorization of 15408 in exponential form is:

15408 = 2⁴ × 3² × 107¹

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 15408

List of positive integer factors of 15408 that divides 15408 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 107, 144, 214, 321, 428, 642, 856, 963, 1284, 1712, 1926, 2568, 3852, 5136, 7704

Step-4: Factors of 15414

List of positive integer factors of 15414 that divides 15408 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 15408 and 15414. The biggest common factor number is the GCF number.
So the greatest common factor 15408 and 15414 is 6.

Also check out the Least Common Multiple of 15408 and 15414