GCF of 874/76, 154/678
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 874/76, 154/678 i.e 2/25764 easily. The following is the detailed procedure to determine the greatest common factor of fractions 874/76, 154/678.
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 874/76,154/678?
Given fractions are 874/76,154/678
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 874/76,154/678, numerators are 874,154
Denominators are 76,678
The GCF of 874,154 is 2 .
LCM of 76,678 is 25764.
The greatest common factor of 874/76,154/678 = [GCF of 874,154]/[LCM of 76,678]= 2/25764
Therefore, the GCF of 874/76,154/678 is 2/25764.
To find the highest common factor of 874,154, we have to find the factors of both numbers and list the highest common factor.
The factors of 874 are 1, 2, 19, 23, 38, 46, 437, 874
The factors of 154 are 1, 2, 7, 11, 14, 22, 77, 154
The HCF of 874,154 is 2.
Lets's calculate GCF of 874,154
| 2 | 874, 154 |
| 437, 77 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 874,154 By Matching Biggest Common Factor Method
Now, list down the factors of 874
:1,2,19,23,38,46,437,874
Now, list down the factors of 154
:1,2,7,11,14,22,77,154
Greatest Common Factor
We found the factors 874,154 . The biggest common factor number is the GCF number.
So the greatest common factor 874,154 is 2.
Lets's calculate LCM of 76,678
| 2 | 76, 678 |
| 38, 339 |
∴ So the LCM of the given numbers is 2 x 38 x 339 = 25764
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/25764
Therefore, the GCF of Fractions 874/76,154/678 is 2/25764
Least Common Multiple of 76,678 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 76,678 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(76,678) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(76,678) x common factors =2 x 1 = 2
LCM(76,678) = ( 76 × 678 ) / 2
LCM(76,678) = 51528 / 2
LCM(76,678) = 25764
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FAQs on GCF of Fractions of 874/76, 154/678
1. What is the HCF of 874,154?
The HCF of 874,154 is 2
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 874/76, 154/678?
Answer: GCF of Numerators as per given numbers 874/76, 154/678 is
GCF of Numerators i.e. for 874,154 is 2
LCM of denominators i.e. for 76,678 is 25764.
Thus, GCF of Fractions is 2/25764.Finally, GCF of Fractions for 874/76, 154/678 is 2/25764.