GCF of 678/48, 846/12, 748/36
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 678/48, 846/12, 748/36 i.e 2/144 easily. The following is the detailed procedure to determine the greatest common factor of fractions 678/48, 846/12, 748/36.
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 678/48,846/12,748/36?
Given fractions are 678/48,846/12,748/36
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 678/48,846/12,748/36, numerators are 678,846,748
Denominators are 48,12,36
The GCF of 678,846,748 is 2 .
LCM of 48,12,36 is 144.
The greatest common factor of 678/48,846/12,748/36 = [GCF of 678,846,748]/[LCM of 48,12,36]= 2/144
Therefore, the GCF of 678/48,846/12,748/36 is 2/144.
To find the highest common factor of 678,846,748, we have to find the factors of both numbers and list the highest common factor.
The factors of 678 are 1, 2, 3, 6, 113, 226, 339, 678
The factors of 846 are 1, 2, 3, 6, 9, 18, 47, 94, 141, 282, 423, 846
The factors of 748 are 1, 2, 4, 11, 17, 22, 34, 44, 68, 187, 374, 748
The HCF of 678,846,748 is 2.
Lets's calculate GCF of 678,846,748
| 2 | 678, 846, 748 |
| 339, 423, 374 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 678,846,748 By Matching Biggest Common Factor Method
Now, list down the factors of 678
:1,2,3,6,113,226,339,678
Now, list down the factors of 846
:1,2,3,6,9,18,47,94,141,282,423,846
Now, list down the factors of 748
:1,2,4,11,17,22,34,44,68,187,374,748
Greatest Common Factor
We found the factors 678,846,748 . The biggest common factor number is the GCF number.
So the greatest common factor 678,846,748 is 2.
Lets's calculate LCM of 48,12,36
| 2 | 48, 12, 36 |
| 2 | 24, 6, 18 |
| 3 | 12, 3, 9 |
| 4, 1, 3 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 4 x 1 x 3 = 144
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/144
Therefore, the GCF of Fractions 678/48,846/12,748/36 is 2/144
Least Common Multiple of 48,12,36 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 48,12,36 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(48,12,36) = 12
common factors(in case of two or more numbers have common factors) = 12
GCF(48,12,36) x common factors =12 x 12 = 144
LCM(48,12,36) = ( 48 × 12 × 36 ) / 144
LCM(48,12,36) = 20736 / 144
LCM(48,12,36) = 144
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 678/48, 846/12, 748/36
1. What is the HCF of 678,846,748?
The HCF of 678,846,748 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 678/48, 846/12, 748/36?
Answer: GCF of Numerators as per given numbers 678/48, 846/12, 748/36 is
GCF of Numerators i.e. for 678,846,748 is 2
LCM of denominators i.e. for 48,12,36 is 144.
Thus, GCF of Fractions is 2/144.Finally, GCF of Fractions for 678/48, 846/12, 748/36 is 2/144.