What is the Greatest Common Factor of 14280 and 14288?

Greatest common factor (GCF) of 14280 and 14288 is 8.

GCF(14280,14288) = 8

We will now calculate the prime factors of 14280 and 14288, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14280 and 14288.

How to find the GCF of 14280 and 14288?

We will first find the prime factorization of 14280 and 14288. After we will calculate the factors of 14280 and 14288 and find the biggest common factor number .

Step-1: Prime Factorization of 14280

Prime factors of 14280 are 2, 3, 5, 7, 17. Prime factorization of 14280 in exponential form is:

14280 = 2³ × 3¹ × 5¹ × 7¹ × 17¹

Step-2: Prime Factorization of 14288

Prime factors of 14288 are 2, 19, 47. Prime factorization of 14288 in exponential form is:

14288 = 2⁴ × 19¹ × 47¹

Step-3: Factors of 14280

List of positive integer factors of 14280 that divides 14280 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 17, 20, 21, 24, 28, 30, 34, 35, 40, 42, 51, 56, 60, 68, 70, 84, 85, 102, 105, 119, 120, 136, 140, 168, 170, 204, 210, 238, 255, 280, 340, 357, 408, 420, 476, 510, 595, 680, 714, 840, 952, 1020, 1190, 1428, 1785, 2040, 2380, 2856, 3570, 4760, 7140

Step-4: Factors of 14288

List of positive integer factors of 14288 that divides 14280 without a remainder.

1, 2, 4, 8, 16, 19, 38, 47, 76, 94, 152, 188, 304, 376, 752, 893, 1786, 3572, 7144

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14280 and 14288. The biggest common factor number is the GCF number.
So the greatest common factor 14280 and 14288 is 8.

Also check out the Least Common Multiple of 14280 and 14288