What is the Greatest Common Factor of 34320 and 34340?

Greatest common factor (GCF) of 34320 and 34340 is 20.

GCF(34320,34340) = 20

We will now calculate the prime factors of 34320 and 34340, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34320 and 34340.

How to find the GCF of 34320 and 34340?

We will first find the prime factorization of 34320 and 34340. After we will calculate the factors of 34320 and 34340 and find the biggest common factor number .

Step-1: Prime Factorization of 34320

Prime factors of 34320 are 2, 3, 5, 11, 13. Prime factorization of 34320 in exponential form is:

34320 = 2⁴ × 3¹ × 5¹ × 11¹ × 13¹

Step-2: Prime Factorization of 34340

Prime factors of 34340 are 2, 5, 17, 101. Prime factorization of 34340 in exponential form is:

34340 = 2² × 5¹ × 17¹ × 101¹

Step-3: Factors of 34320

List of positive integer factors of 34320 that divides 34320 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 13, 15, 16, 20, 22, 24, 26, 30, 33, 39, 40, 44, 48, 52, 55, 60, 65, 66, 78, 80, 88, 104, 110, 120, 130, 132, 143, 156, 165, 176, 195, 208, 220, 240, 260, 264, 286, 312, 330, 390, 429, 440, 520, 528, 572, 624, 660, 715, 780, 858, 880, 1040, 1144, 1320, 1430, 1560, 1716, 2145, 2288, 2640, 2860, 3120, 3432, 4290, 5720, 6864, 8580, 11440, 17160

Step-4: Factors of 34340

List of positive integer factors of 34340 that divides 34320 without a remainder.

1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 101, 170, 202, 340, 404, 505, 1010, 1717, 2020, 3434, 6868, 8585, 17170

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34320 and 34340. The biggest common factor number is the GCF number.
So the greatest common factor 34320 and 34340 is 20.

Also check out the Least Common Multiple of 34320 and 34340