What is the Greatest Common Factor of 5040 and 5050?

Greatest common factor (GCF) of 5040 and 5050 is 10.

GCF(5040,5050) = 10

We will now calculate the prime factors of 5040 and 5050, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5040 and 5050.

How to find the GCF of 5040 and 5050?

We will first find the prime factorization of 5040 and 5050. After we will calculate the factors of 5040 and 5050 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 5050

Prime factors of 5050 are 2, 5, 101. Prime factorization of 5050 in exponential form is:

5050 = 2¹ × 5² × 101¹

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 5050

List of positive integer factors of 5050 that divides 5040 without a remainder.

1, 2, 5, 10, 25, 50, 101, 202, 505, 1010, 2525

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5040 and 5050. The biggest common factor number is the GCF number.
So the greatest common factor 5040 and 5050 is 10.

Also check out the Least Common Multiple of 5040 and 5050