What is the Greatest Common Factor of 23513 and 23520?

Greatest common factor (GCF) of 23513 and 23520 is 7.

GCF(23513,23520) = 7

We will now calculate the prime factors of 23513 and 23520, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 23513 and 23520.

How to find the GCF of 23513 and 23520?

We will first find the prime factorization of 23513 and 23520. After we will calculate the factors of 23513 and 23520 and find the biggest common factor number .

Step-1: Prime Factorization of 23513

Prime factors of 23513 are 7, 3359. Prime factorization of 23513 in exponential form is:

23513 = 7¹ × 3359¹

Step-2: Prime Factorization of 23520

Prime factors of 23520 are 2, 3, 5, 7. Prime factorization of 23520 in exponential form is:

23520 = 2⁵ × 3¹ × 5¹ × 7²

Step-3: Factors of 23513

List of positive integer factors of 23513 that divides 23513 without a remainder.

1, 7, 3359

Step-4: Factors of 23520

List of positive integer factors of 23520 that divides 23513 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 32, 35, 40, 42, 48, 49, 56, 60, 70, 80, 84, 96, 98, 105, 112, 120, 140, 147, 160, 168, 196, 210, 224, 240, 245, 280, 294, 336, 392, 420, 480, 490, 560, 588, 672, 735, 784, 840, 980, 1120, 1176, 1470, 1568, 1680, 1960, 2352, 2940, 3360, 3920, 4704, 5880, 7840, 11760

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 23513 and 23520. The biggest common factor number is the GCF number.
So the greatest common factor 23513 and 23520 is 7.

Also check out the Least Common Multiple of 23513 and 23520