What is the Greatest Common Factor of 90714 and 90720?

Greatest common factor (GCF) of 90714 and 90720 is 6.

GCF(90714,90720) = 6

We will now calculate the prime factors of 90714 and 90720, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 90714 and 90720.

How to find the GCF of 90714 and 90720?

We will first find the prime factorization of 90714 and 90720. After we will calculate the factors of 90714 and 90720 and find the biggest common factor number .

Step-1: Prime Factorization of 90714

Prime factors of 90714 are 2, 3, 13, 1163. Prime factorization of 90714 in exponential form is:

90714 = 2¹ × 3¹ × 13¹ × 1163¹

Step-2: Prime Factorization of 90720

Prime factors of 90720 are 2, 3, 5, 7. Prime factorization of 90720 in exponential form is:

90720 = 2⁵ × 3⁴ × 5¹ × 7¹

Step-3: Factors of 90714

List of positive integer factors of 90714 that divides 90714 without a remainder.

1, 2, 3, 6, 13, 26, 39, 78, 1163, 2326, 3489, 6978, 15119, 30238, 45357

Step-4: Factors of 90720

List of positive integer factors of 90720 that divides 90714 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 27, 28, 30, 32, 35, 36, 40, 42, 45, 48, 54, 56, 60, 63, 70, 72, 80, 81, 84, 90, 96, 105, 108, 112, 120, 126, 135, 140, 144, 160, 162, 168, 180, 189, 210, 216, 224, 240, 252, 270, 280, 288, 315, 324, 336, 360, 378, 405, 420, 432, 480, 504, 540, 560, 567, 630, 648, 672, 720, 756, 810, 840, 864, 945, 1008, 1080, 1120, 1134, 1260, 1296, 1440, 1512, 1620, 1680, 1890, 2016, 2160, 2268, 2520, 2592, 2835, 3024, 3240, 3360, 3780, 4320, 4536, 5040, 5670, 6048, 6480, 7560, 9072, 10080, 11340, 12960, 15120, 18144, 22680, 30240, 45360

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 90714 and 90720. The biggest common factor number is the GCF number.
So the greatest common factor 90714 and 90720 is 6.

Also check out the Least Common Multiple of 90714 and 90720