What is the Greatest Common Factor of 78523 and 78540?

Greatest common factor (GCF) of 78523 and 78540 is 17.

GCF(78523,78540) = 17

We will now calculate the prime factors of 78523 and 78540, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 78523 and 78540.

How to find the GCF of 78523 and 78540?

We will first find the prime factorization of 78523 and 78540. After we will calculate the factors of 78523 and 78540 and find the biggest common factor number .

Step-1: Prime Factorization of 78523

Prime factors of 78523 are 17, 31, 149. Prime factorization of 78523 in exponential form is:

78523 = 17¹ × 31¹ × 149¹

Step-2: Prime Factorization of 78540

Prime factors of 78540 are 2, 3, 5, 7, 11, 17. Prime factorization of 78540 in exponential form is:

78540 = 2² × 3¹ × 5¹ × 7¹ × 11¹ × 17¹

Step-3: Factors of 78523

List of positive integer factors of 78523 that divides 78523 without a remainder.

1, 17, 31, 149, 527, 2533, 4619

Step-4: Factors of 78540

List of positive integer factors of 78540 that divides 78523 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 14, 15, 17, 20, 21, 22, 28, 30, 33, 34, 35, 42, 44, 51, 55, 60, 66, 68, 70, 77, 84, 85, 102, 105, 110, 119, 132, 140, 154, 165, 170, 187, 204, 210, 220, 231, 238, 255, 308, 330, 340, 357, 374, 385, 420, 462, 476, 510, 561, 595, 660, 714, 748, 770, 924, 935, 1020, 1122, 1155, 1190, 1309, 1428, 1540, 1785, 1870, 2244, 2310, 2380, 2618, 2805, 3570, 3740, 3927, 4620, 5236, 5610, 6545, 7140, 7854, 11220, 13090, 15708, 19635, 26180, 39270

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 78523 and 78540. The biggest common factor number is the GCF number.
So the greatest common factor 78523 and 78540 is 17.

Also check out the Least Common Multiple of 78523 and 78540