What is the Greatest Common Factor of 289 and 296?
Greatest common factor (GCF) of 289 and 296 is 1.
GCF(289,296) = 1
We will now calculate the prime factors of 289 and 296, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 289 and 296.
How to find the GCF of 289 and 296?
We will first find the prime factorization of 289 and 296. After we will calculate the factors of 289 and 296 and find the biggest common factor number .
Step-1: Prime Factorization of 289
Prime factors of 289 are 17. Prime factorization of 289 in exponential form is:
289 = 172
Step-2: Prime Factorization of 296
Prime factors of 296 are 2, 37. Prime factorization of 296 in exponential form is:
296 = 23 × 371
Step-3: Factors of 289
List of positive integer factors of 289 that divides 289 without a remainder.
1, 17
Step-4: Factors of 296
List of positive integer factors of 296 that divides 289 without a remainder.
1, 2, 4, 8, 37, 74, 148
Final Step: Biggest Common Factor Number
We found the factors and prime factorization of 289 and 296. The biggest common factor number is the GCF number.
So the greatest common factor 289 and 296 is 1.
Also check out the Least Common Multiple of 289 and 296
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