GCF of 656/60, 762/174
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 656/60, 762/174 i.e 2/1740 easily. The following is the detailed procedure to determine the greatest common factor of fractions 656/60, 762/174.
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 656/60,762/174?
Given fractions are 656/60,762/174
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 656/60,762/174, numerators are 656,762
Denominators are 60,174
The GCF of 656,762 is 2 .
LCM of 60,174 is 1740.
The greatest common factor of 656/60,762/174 = [GCF of 656,762]/[LCM of 60,174]= 2/1740
Therefore, the GCF of 656/60,762/174 is 2/1740.
To find the highest common factor of 656,762, we have to find the factors of both numbers and list the highest common factor.
The factors of 656 are 1, 2, 4, 8, 16, 41, 82, 164, 328, 656
The factors of 762 are 1, 2, 3, 6, 127, 254, 381, 762
The HCF of 656,762 is 2.
Lets's calculate GCF of 656,762
| 2 | 656, 762 |
| 328, 381 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 656,762 By Matching Biggest Common Factor Method
Now, list down the factors of 656
:1,2,4,8,16,41,82,164,328,656
Now, list down the factors of 762
:1,2,3,6,127,254,381,762
Greatest Common Factor
We found the factors 656,762 . The biggest common factor number is the GCF number.
So the greatest common factor 656,762 is 2.
Lets's calculate LCM of 60,174
| 2 | 60, 174 |
| 3 | 30, 87 |
| 10, 29 |
∴ So the LCM of the given numbers is 2 x 3 x 10 x 29 = 1740
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1740
Therefore, the GCF of Fractions 656/60,762/174 is 2/1740
Least Common Multiple of 60,174 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 60,174 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(60,174) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(60,174) x common factors =6 x 1 = 6
LCM(60,174) = ( 60 × 174 ) / 6
LCM(60,174) = 10440 / 6
LCM(60,174) = 1740
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FAQs on GCF of Fractions of 656/60, 762/174
1. What is the HCF of 656,762?
The HCF of 656,762 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 656/60, 762/174?
Answer: GCF of Numerators as per given numbers 656/60, 762/174 is
GCF of Numerators i.e. for 656,762 is 2
LCM of denominators i.e. for 60,174 is 1740.
Thus, GCF of Fractions is 2/1740.Finally, GCF of Fractions for 656/60, 762/174 is 2/1740.