What is the Greatest Common Factor of 7038 and 7056?

Greatest common factor (GCF) of 7038 and 7056 is 18.

GCF(7038,7056) = 18

We will now calculate the prime factors of 7038 and 7056, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7038 and 7056.

How to find the GCF of 7038 and 7056?

We will first find the prime factorization of 7038 and 7056. After we will calculate the factors of 7038 and 7056 and find the biggest common factor number .

Step-1: Prime Factorization of 7038

Prime factors of 7038 are 2, 3, 17, 23. Prime factorization of 7038 in exponential form is:

7038 = 2¹ × 3² × 17¹ × 23¹

Step-2: Prime Factorization of 7056

Prime factors of 7056 are 2, 3, 7. Prime factorization of 7056 in exponential form is:

7056 = 2⁴ × 3² × 7²

Step-3: Factors of 7038

List of positive integer factors of 7038 that divides 7038 without a remainder.

1, 2, 3, 6, 9, 17, 18, 23, 34, 46, 51, 69, 102, 138, 153, 207, 306, 391, 414, 782, 1173, 2346, 3519

Step-4: Factors of 7056

List of positive integer factors of 7056 that divides 7038 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 49, 56, 63, 72, 84, 98, 112, 126, 144, 147, 168, 196, 252, 294, 336, 392, 441, 504, 588, 784, 882, 1008, 1176, 1764, 2352, 3528

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7038 and 7056. The biggest common factor number is the GCF number.
So the greatest common factor 7038 and 7056 is 18.

Also check out the Least Common Multiple of 7038 and 7056