GCF of 1278/502, 1961/7678
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1278/502, 1961/7678 i.e 1/1927178 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1278/502, 1961/7678.
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 1278/502,1961/7678?
Given fractions are 1278/502,1961/7678
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 1278/502,1961/7678, numerators are 1278,1961
Denominators are 502,7678
The GCF of 1278,1961 is 1 .
LCM of 502,7678 is 1927178.
The greatest common factor of 1278/502,1961/7678 = [GCF of 1278,1961]/[LCM of 502,7678]= 1/1927178
Therefore, the GCF of 1278/502,1961/7678 is 1/1927178.
To find the highest common factor of 1278,1961, we have to find the factors of both numbers and list the highest common factor.
The factors of 1278 are 1, 2, 3, 6, 9, 18, 71, 142, 213, 426, 639, 1278
The factors of 1961 are 1, 37, 53, 1961
The HCF of 1278,1961 is 1.
Lets's calculate GCF of 1278,1961
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 1278,1961 By Matching Biggest Common Factor Method
Now, list down the factors of 1278
:1,2,3,6,9,18,71,142,213,426,639,1278
Now, list down the factors of 1961
:1,37,53,1961
Greatest Common Factor
We found the factors 1278,1961 . The biggest common factor number is the GCF number.
So the greatest common factor 1278,1961 is 1.
Lets's calculate LCM of 502,7678
| 2 | 502, 7678 |
| 251, 3839 |
∴ So the LCM of the given numbers is 2 x 251 x 3839 = 1927178
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1927178
Therefore, the GCF of Fractions 1278/502,1961/7678 is 1/1927178
Least Common Multiple of 502,7678 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 502,7678 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(502,7678) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(502,7678) x common factors =2 x 1 = 2
LCM(502,7678) = ( 502 × 7678 ) / 2
LCM(502,7678) = 3854356 / 2
LCM(502,7678) = 1927178
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FAQs on GCF of Fractions of 1278/502, 1961/7678
1. What is the HCF of 1278,1961?
The HCF of 1278,1961 is 1
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 1278/502, 1961/7678?
Answer: GCF of Numerators as per given numbers 1278/502, 1961/7678 is
GCF of Numerators i.e. for 1278,1961 is 1
LCM of denominators i.e. for 502,7678 is 1927178.
Thus, GCF of Fractions is 1/1927178.Finally, GCF of Fractions for 1278/502, 1961/7678 is 1/1927178.