GCF of 747/420, 675/168
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 747/420, 675/168 i.e 9/840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 747/420, 675/168.
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 747/420,675/168?
Given fractions are 747/420,675/168
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 747/420,675/168, numerators are 747,675
Denominators are 420,168
The GCF of 747,675 is 9 .
LCM of 420,168 is 840.
The greatest common factor of 747/420,675/168 = [GCF of 747,675]/[LCM of 420,168]= 9/840
Therefore, the GCF of 747/420,675/168 is 9/840.
To find the highest common factor of 747,675, we have to find the factors of both numbers and list the highest common factor.
The factors of 747 are 1, 3, 9, 83, 249, 747
The factors of 675 are 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675
The HCF of 747,675 is 9.
Lets's calculate GCF of 747,675
| 3 | 747, 675 |
| 3 | 249, 225 |
| 83, 75 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Greatest Common Factor of 747,675 By Matching Biggest Common Factor Method
Now, list down the factors of 747
:1,3,9,83,249,747
Now, list down the factors of 675
:1,3,5,9,15,25,27,45,75,135,225,675
Greatest Common Factor
We found the factors 747,675 . The biggest common factor number is the GCF number.
So the greatest common factor 747,675 is 9.
Lets's calculate LCM of 420,168
| 2 | 420, 168 |
| 2 | 210, 84 |
| 3 | 105, 42 |
| 7 | 35, 14 |
| 5, 2 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 7 x 5 x 2 = 840
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/840
Therefore, the GCF of Fractions 747/420,675/168 is 9/840
Least Common Multiple of 420,168 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 420,168 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(420,168) = 84
common factors(in case of two or more numbers have common factors) = 1
GCF(420,168) x common factors =84 x 1 = 84
LCM(420,168) = ( 420 × 168 ) / 84
LCM(420,168) = 70560 / 84
LCM(420,168) = 840
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FAQs on GCF of Fractions of 747/420, 675/168
1. What is the HCF of 747,675?
The HCF of 747,675 is 9
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 747/420, 675/168?
Answer: GCF of Numerators as per given numbers 747/420, 675/168 is
GCF of Numerators i.e. for 747,675 is 9
LCM of denominators i.e. for 420,168 is 840.
Thus, GCF of Fractions is 9/840.Finally, GCF of Fractions for 747/420, 675/168 is 9/840.