What is the Greatest Common Factor of 10523 and 10540?

Greatest common factor (GCF) of 10523 and 10540 is 17.

GCF(10523,10540) = 17

We will now calculate the prime factors of 10523 and 10540, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10523 and 10540.

How to find the GCF of 10523 and 10540?

We will first find the prime factorization of 10523 and 10540. After we will calculate the factors of 10523 and 10540 and find the biggest common factor number .

Step-1: Prime Factorization of 10523

Prime factors of 10523 are 17, 619. Prime factorization of 10523 in exponential form is:

10523 = 17¹ × 619¹

Step-2: Prime Factorization of 10540

Prime factors of 10540 are 2, 5, 17, 31. Prime factorization of 10540 in exponential form is:

10540 = 2² × 5¹ × 17¹ × 31¹

Step-3: Factors of 10523

List of positive integer factors of 10523 that divides 10523 without a remainder.

1, 17, 619

Step-4: Factors of 10540

List of positive integer factors of 10540 that divides 10523 without a remainder.

1, 2, 4, 5, 10, 17, 20, 31, 34, 62, 68, 85, 124, 155, 170, 310, 340, 527, 620, 1054, 2108, 2635, 5270

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10523 and 10540. The biggest common factor number is the GCF number.
So the greatest common factor 10523 and 10540 is 17.

Also check out the Least Common Multiple of 10523 and 10540