GCF of 108/77, 282/457
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 108/77, 282/457 i.e 6/35189 easily. The following is the detailed procedure to determine the greatest common factor of fractions 108/77, 282/457.
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 108/77,282/457?
Given fractions are 108/77,282/457
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 108/77,282/457, numerators are 108,282
Denominators are 77,457
The GCF of 108,282 is 6 .
LCM of 77,457 is 35189.
The greatest common factor of 108/77,282/457 = [GCF of 108,282]/[LCM of 77,457]= 6/35189
Therefore, the GCF of 108/77,282/457 is 6/35189.
To find the highest common factor of 108,282, we have to find the factors of both numbers and list the highest common factor.
The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
The factors of 282 are 1, 2, 3, 6, 47, 94, 141, 282
The HCF of 108,282 is 6.
Lets's calculate GCF of 108,282
| 2 | 108, 282 |
| 3 | 54, 141 |
| 18, 47 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 108,282 By Matching Biggest Common Factor Method
Now, list down the factors of 108
:1,2,3,4,6,9,12,18,27,36,54,108
Now, list down the factors of 282
:1,2,3,6,47,94,141,282
Greatest Common Factor
We found the factors 108,282 . The biggest common factor number is the GCF number.
So the greatest common factor 108,282 is 6.
Lets's calculate LCM of 77,457
Given numbers has no common factors except 1. So, there LCM is their product i.e 35189
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/35189
Therefore, the GCF of Fractions 108/77,282/457 is 6/35189
Least Common Multiple of 77,457 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 77,457 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(77,457) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(77,457) x common factors =1 x 1 = 1
LCM(77,457) = ( 77 × 457 ) / 1
LCM(77,457) = 35189 / 1
LCM(77,457) = 35189
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FAQs on GCF of Fractions of 108/77, 282/457
1. What is the HCF of 108,282?
The HCF of 108,282 is 6
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 108/77, 282/457?
Answer: GCF of Numerators as per given numbers 108/77, 282/457 is
GCF of Numerators i.e. for 108,282 is 6
LCM of denominators i.e. for 77,457 is 35189.
Thus, GCF of Fractions is 6/35189.Finally, GCF of Fractions for 108/77, 282/457 is 6/35189.