What is the Greatest Common Factor of 95200 and 95214?

Greatest common factor (GCF) of 95200 and 95214 is 14.

GCF(95200,95214) = 14

We will now calculate the prime factors of 95200 and 95214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 95200 and 95214.

How to find the GCF of 95200 and 95214?

We will first find the prime factorization of 95200 and 95214. After we will calculate the factors of 95200 and 95214 and find the biggest common factor number .

Step-1: Prime Factorization of 95200

Prime factors of 95200 are 2, 5, 7, 17. Prime factorization of 95200 in exponential form is:

95200 = 2⁵ × 5² × 7¹ × 17¹

Step-2: Prime Factorization of 95214

Prime factors of 95214 are 2, 3, 7, 2267. Prime factorization of 95214 in exponential form is:

95214 = 2¹ × 3¹ × 7¹ × 2267¹

Step-3: Factors of 95200

List of positive integer factors of 95200 that divides 95200 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 17, 20, 25, 28, 32, 34, 35, 40, 50, 56, 68, 70, 80, 85, 100, 112, 119, 136, 140, 160, 170, 175, 200, 224, 238, 272, 280, 340, 350, 400, 425, 476, 544, 560, 595, 680, 700, 800, 850, 952, 1120, 1190, 1360, 1400, 1700, 1904, 2380, 2720, 2800, 2975, 3400, 3808, 4760, 5600, 5950, 6800, 9520, 11900, 13600, 19040, 23800, 47600

Step-4: Factors of 95214

List of positive integer factors of 95214 that divides 95200 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 2267, 4534, 6801, 13602, 15869, 31738, 47607

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 95200 and 95214. The biggest common factor number is the GCF number.
So the greatest common factor 95200 and 95214 is 14.

Also check out the Least Common Multiple of 95200 and 95214