GCF of 748/36, 678/1966
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 748/36, 678/1966 i.e 2/35388 easily. The following is the detailed procedure to determine the greatest common factor of fractions 748/36, 678/1966.
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 748/36,678/1966?
Given fractions are 748/36,678/1966
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 748/36,678/1966, numerators are 748,678
Denominators are 36,1966
The GCF of 748,678 is 2 .
LCM of 36,1966 is 35388.
The greatest common factor of 748/36,678/1966 = [GCF of 748,678]/[LCM of 36,1966]= 2/35388
Therefore, the GCF of 748/36,678/1966 is 2/35388.
To find the highest common factor of 748,678, we have to find the factors of both numbers and list the highest common factor.
The factors of 748 are 1, 2, 4, 11, 17, 22, 34, 44, 68, 187, 374, 748
The factors of 678 are 1, 2, 3, 6, 113, 226, 339, 678
The HCF of 748,678 is 2.
Lets's calculate GCF of 748,678
| 2 | 748, 678 |
| 374, 339 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 748,678 By Matching Biggest Common Factor Method
Now, list down the factors of 748
:1,2,4,11,17,22,34,44,68,187,374,748
Now, list down the factors of 678
:1,2,3,6,113,226,339,678
Greatest Common Factor
We found the factors 748,678 . The biggest common factor number is the GCF number.
So the greatest common factor 748,678 is 2.
Lets's calculate LCM of 36,1966
| 2 | 36, 1966 |
| 18, 983 |
∴ So the LCM of the given numbers is 2 x 18 x 983 = 35388
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/35388
Therefore, the GCF of Fractions 748/36,678/1966 is 2/35388
Least Common Multiple of 36,1966 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 36,1966 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(36,1966) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(36,1966) x common factors =2 x 1 = 2
LCM(36,1966) = ( 36 × 1966 ) / 2
LCM(36,1966) = 70776 / 2
LCM(36,1966) = 35388
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FAQs on GCF of Fractions of 748/36, 678/1966
1. What is the HCF of 748,678?
The HCF of 748,678 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 748/36, 678/1966?
Answer: GCF of Numerators as per given numbers 748/36, 678/1966 is
GCF of Numerators i.e. for 748,678 is 2
LCM of denominators i.e. for 36,1966 is 35388.
Thus, GCF of Fractions is 2/35388.Finally, GCF of Fractions for 748/36, 678/1966 is 2/35388.