What is the Greatest Common Factor of 7140 and 7148?

Greatest common factor (GCF) of 7140 and 7148 is 4.

GCF(7140,7148) = 4

We will now calculate the prime factors of 7140 and 7148, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7140 and 7148.

How to find the GCF of 7140 and 7148?

We will first find the prime factorization of 7140 and 7148. After we will calculate the factors of 7140 and 7148 and find the biggest common factor number .

Step-1: Prime Factorization of 7140

Prime factors of 7140 are 2, 3, 5, 7, 17. Prime factorization of 7140 in exponential form is:

7140 = 2² × 3¹ × 5¹ × 7¹ × 17¹

Step-2: Prime Factorization of 7148

Prime factors of 7148 are 2, 1787. Prime factorization of 7148 in exponential form is:

7148 = 2² × 1787¹

Step-3: Factors of 7140

List of positive integer factors of 7140 that divides 7140 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 17, 20, 21, 28, 30, 34, 35, 42, 51, 60, 68, 70, 84, 85, 102, 105, 119, 140, 170, 204, 210, 238, 255, 340, 357, 420, 476, 510, 595, 714, 1020, 1190, 1428, 1785, 2380, 3570

Step-4: Factors of 7148

List of positive integer factors of 7148 that divides 7140 without a remainder.

1, 2, 4, 1787, 3574

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7140 and 7148. The biggest common factor number is the GCF number.
So the greatest common factor 7140 and 7148 is 4.

Also check out the Least Common Multiple of 7140 and 7148