GCF of 42/39, 774/14, 688/546
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 42/39, 774/14, 688/546 i.e 2/546 easily. The following is the detailed procedure to determine the greatest common factor of fractions 42/39, 774/14, 688/546.
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 42/39,774/14,688/546?
Given fractions are 42/39,774/14,688/546
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 42/39,774/14,688/546, numerators are 42,774,688
Denominators are 39,14,546
The GCF of 42,774,688 is 2 .
LCM of 39,14,546 is 546.
The greatest common factor of 42/39,774/14,688/546 = [GCF of 42,774,688]/[LCM of 39,14,546]= 2/546
Therefore, the GCF of 42/39,774/14,688/546 is 2/546.
To find the highest common factor of 42,774,688, we have to find the factors of both numbers and list the highest common factor.
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 774 are 1, 2, 3, 6, 9, 18, 43, 86, 129, 258, 387, 774
The factors of 688 are 1, 2, 4, 8, 16, 43, 86, 172, 344, 688
The HCF of 42,774,688 is 2.
Lets's calculate GCF of 42,774,688
| 2 | 42, 774, 688 |
| 21, 387, 344 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 42,774,688 By Matching Biggest Common Factor Method
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Now, list down the factors of 774
:1,2,3,6,9,18,43,86,129,258,387,774
Now, list down the factors of 688
:1,2,4,8,16,43,86,172,344,688
Greatest Common Factor
We found the factors 42,774,688 . The biggest common factor number is the GCF number.
So the greatest common factor 42,774,688 is 2.
Lets's calculate LCM of 39,14,546
| 2 | 39, 14, 546 |
| 3 | 39, 7, 273 |
| 7 | 13, 7, 91 |
| 13 | 13, 1, 13 |
| 1, 1, 1 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 13 x 1 x 1 x 1 = 546
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/546
Therefore, the GCF of Fractions 42/39,774/14,688/546 is 2/546
Least Common Multiple of 39,14,546 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 39,14,546 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(39,14,546) = 1
common factors(in case of two or more numbers have common factors) = 546
GCF(39,14,546) x common factors =1 x 546 = 546
LCM(39,14,546) = ( 39 × 14 × 546 ) / 546
LCM(39,14,546) = 298116 / 546
LCM(39,14,546) = 546
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 42/39, 774/14, 688/546
1. What is the HCF of 42,774,688?
The HCF of 42,774,688 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 42/39, 774/14, 688/546?
Answer: GCF of Numerators as per given numbers 42/39, 774/14, 688/546 is
GCF of Numerators i.e. for 42,774,688 is 2
LCM of denominators i.e. for 39,14,546 is 546.
Thus, GCF of Fractions is 2/546.Finally, GCF of Fractions for 42/39, 774/14, 688/546 is 2/546.