What is the Greatest Common Factor of 5083 and 5100?

Greatest common factor (GCF) of 5083 and 5100 is 17.

GCF(5083,5100) = 17

We will now calculate the prime factors of 5083 and 5100, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5083 and 5100.

How to find the GCF of 5083 and 5100?

We will first find the prime factorization of 5083 and 5100. After we will calculate the factors of 5083 and 5100 and find the biggest common factor number .

Step-1: Prime Factorization of 5083

Prime factors of 5083 are 13, 17, 23. Prime factorization of 5083 in exponential form is:

5083 = 13¹ × 17¹ × 23¹

Step-2: Prime Factorization of 5100

Prime factors of 5100 are 2, 3, 5, 17. Prime factorization of 5100 in exponential form is:

5100 = 2² × 3¹ × 5² × 17¹

Step-3: Factors of 5083

List of positive integer factors of 5083 that divides 5083 without a remainder.

1, 13, 17, 23, 221, 299, 391

Step-4: Factors of 5100

List of positive integer factors of 5100 that divides 5083 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 17, 20, 25, 30, 34, 50, 51, 60, 68, 75, 85, 100, 102, 150, 170, 204, 255, 300, 340, 425, 510, 850, 1020, 1275, 1700, 2550

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5083 and 5100. The biggest common factor number is the GCF number.
So the greatest common factor 5083 and 5100 is 17.

Also check out the Least Common Multiple of 5083 and 5100