GCF of 914/42, 688/6702
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 914/42, 688/6702 i.e 2/46914 easily. The following is the detailed procedure to determine the greatest common factor of fractions 914/42, 688/6702.
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 914/42,688/6702?
Given fractions are 914/42,688/6702
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 914/42,688/6702, numerators are 914,688
Denominators are 42,6702
The GCF of 914,688 is 2 .
LCM of 42,6702 is 46914.
The greatest common factor of 914/42,688/6702 = [GCF of 914,688]/[LCM of 42,6702]= 2/46914
Therefore, the GCF of 914/42,688/6702 is 2/46914.
To find the highest common factor of 914,688, we have to find the factors of both numbers and list the highest common factor.
The factors of 914 are 1, 2, 457, 914
The factors of 688 are 1, 2, 4, 8, 16, 43, 86, 172, 344, 688
The HCF of 914,688 is 2.
Lets's calculate GCF of 914,688
| 2 | 914, 688 |
| 457, 344 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 914,688 By Matching Biggest Common Factor Method
Now, list down the factors of 914
:1,2,457,914
Now, list down the factors of 688
:1,2,4,8,16,43,86,172,344,688
Greatest Common Factor
We found the factors 914,688 . The biggest common factor number is the GCF number.
So the greatest common factor 914,688 is 2.
Lets's calculate LCM of 42,6702
| 2 | 42, 6702 |
| 3 | 21, 3351 |
| 7, 1117 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 1117 = 46914
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/46914
Therefore, the GCF of Fractions 914/42,688/6702 is 2/46914
Least Common Multiple of 42,6702 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 42,6702 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,6702) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(42,6702) x common factors =6 x 1 = 6
LCM(42,6702) = ( 42 × 6702 ) / 6
LCM(42,6702) = 281484 / 6
LCM(42,6702) = 46914
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FAQs on GCF of Fractions of 914/42, 688/6702
1. What is the HCF of 914,688?
The HCF of 914,688 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 914/42, 688/6702?
Answer: GCF of Numerators as per given numbers 914/42, 688/6702 is
GCF of Numerators i.e. for 914,688 is 2
LCM of denominators i.e. for 42,6702 is 46914.
Thus, GCF of Fractions is 2/46914.Finally, GCF of Fractions for 914/42, 688/6702 is 2/46914.