What is the Greatest Common Factor of 5040 and 5054?

Greatest common factor (GCF) of 5040 and 5054 is 14.

GCF(5040,5054) = 14

We will now calculate the prime factors of 5040 and 5054, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5040 and 5054.

How to find the GCF of 5040 and 5054?

We will first find the prime factorization of 5040 and 5054. After we will calculate the factors of 5040 and 5054 and find the biggest common factor number .

Step-1: Prime Factorization of 5040

Prime factors of 5040 are 2, 3, 5, 7. Prime factorization of 5040 in exponential form is:

5040 = 2⁴ × 3² × 5¹ × 7¹

Step-2: Prime Factorization of 5054

Prime factors of 5054 are 2, 7, 19. Prime factorization of 5054 in exponential form is:

5054 = 2¹ × 7¹ × 19²

Step-3: Factors of 5040

List of positive integer factors of 5040 that divides 5040 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 48, 56, 60, 63, 70, 72, 80, 84, 90, 105, 112, 120, 126, 140, 144, 168, 180, 210, 240, 252, 280, 315, 336, 360, 420, 504, 560, 630, 720, 840, 1008, 1260, 1680, 2520

Step-4: Factors of 5054

List of positive integer factors of 5054 that divides 5040 without a remainder.

1, 2, 7, 14, 19, 38, 133, 266, 361, 722, 2527

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5040 and 5054. The biggest common factor number is the GCF number.
So the greatest common factor 5040 and 5054 is 14.

Also check out the Least Common Multiple of 5040 and 5054