GCF of 364/68, 217/762
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 364/68, 217/762 i.e 7/25908 easily. The following is the detailed procedure to determine the greatest common factor of fractions 364/68, 217/762.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 364/68,217/762?
Given fractions are 364/68,217/762
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 364/68,217/762, numerators are 364,217
Denominators are 68,762
The GCF of 364,217 is 7 .
LCM of 68,762 is 25908.
The greatest common factor of 364/68,217/762 = [GCF of 364,217]/[LCM of 68,762]= 7/25908
Therefore, the GCF of 364/68,217/762 is 7/25908.
To find the highest common factor of 364,217, we have to find the factors of both numbers and list the highest common factor.
The factors of 364 are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364
The factors of 217 are 1, 7, 31, 217
The HCF of 364,217 is 7.
Lets's calculate GCF of 364,217
| 7 | 364, 217 |
| 52, 31 |
∴ So the GCF of the given numbers is 7 = 7
Greatest Common Factor of 364,217 By Matching Biggest Common Factor Method
Now, list down the factors of 364
:1,2,4,7,13,14,26,28,52,91,182,364
Now, list down the factors of 217
:1,7,31,217
Greatest Common Factor
We found the factors 364,217 . The biggest common factor number is the GCF number.
So the greatest common factor 364,217 is 7.
Lets's calculate LCM of 68,762
| 2 | 68, 762 |
| 34, 381 |
∴ So the LCM of the given numbers is 2 x 34 x 381 = 25908
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/25908
Therefore, the GCF of Fractions 364/68,217/762 is 7/25908
Least Common Multiple of 68,762 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 68,762 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(68,762) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(68,762) x common factors =2 x 1 = 2
LCM(68,762) = ( 68 × 762 ) / 2
LCM(68,762) = 51816 / 2
LCM(68,762) = 25908
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FAQs on GCF of Fractions of 364/68, 217/762
1. What is the HCF of 364,217?
The HCF of 364,217 is 7
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 364/68, 217/762?
Answer: GCF of Numerators as per given numbers 364/68, 217/762 is
GCF of Numerators i.e. for 364,217 is 7
LCM of denominators i.e. for 68,762 is 25908.
Thus, GCF of Fractions is 7/25908.Finally, GCF of Fractions for 364/68, 217/762 is 7/25908.