GCF of 717/42, 420/972
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 717/42, 420/972 i.e 3/6804 easily. The following is the detailed procedure to determine the greatest common factor of fractions 717/42, 420/972.
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 717/42,420/972?
Given fractions are 717/42,420/972
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 717/42,420/972, numerators are 717,420
Denominators are 42,972
The GCF of 717,420 is 3 .
LCM of 42,972 is 6804.
The greatest common factor of 717/42,420/972 = [GCF of 717,420]/[LCM of 42,972]= 3/6804
Therefore, the GCF of 717/42,420/972 is 3/6804.
To find the highest common factor of 717,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 717 are 1, 3, 239, 717
The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
The HCF of 717,420 is 3.
Lets's calculate GCF of 717,420
| 3 | 717, 420 |
| 239, 140 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 717,420 By Matching Biggest Common Factor Method
Now, list down the factors of 717
:1,3,239,717
Now, list down the factors of 420
:1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Greatest Common Factor
We found the factors 717,420 . The biggest common factor number is the GCF number.
So the greatest common factor 717,420 is 3.
Lets's calculate LCM of 42,972
| 2 | 42, 972 |
| 3 | 21, 486 |
| 7, 162 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 162 = 6804
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/6804
Therefore, the GCF of Fractions 717/42,420/972 is 3/6804
Least Common Multiple of 42,972 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 42,972 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,972) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(42,972) x common factors =6 x 1 = 6
LCM(42,972) = ( 42 × 972 ) / 6
LCM(42,972) = 40824 / 6
LCM(42,972) = 6804
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FAQs on GCF of Fractions of 717/42, 420/972
1. What is the HCF of 717,420?
The HCF of 717,420 is 3
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 717/42, 420/972?
Answer: GCF of Numerators as per given numbers 717/42, 420/972 is
GCF of Numerators i.e. for 717,420 is 3
LCM of denominators i.e. for 42,972 is 6804.
Thus, GCF of Fractions is 3/6804.Finally, GCF of Fractions for 717/42, 420/972 is 3/6804.