GCF of 272/77, 420/359
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 272/77, 420/359 i.e 4/27643 easily. The following is the detailed procedure to determine the greatest common factor of fractions 272/77, 420/359.
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 272/77,420/359?
Given fractions are 272/77,420/359
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 272/77,420/359, numerators are 272,420
Denominators are 77,359
The GCF of 272,420 is 4 .
LCM of 77,359 is 27643.
The greatest common factor of 272/77,420/359 = [GCF of 272,420]/[LCM of 77,359]= 4/27643
Therefore, the GCF of 272/77,420/359 is 4/27643.
To find the highest common factor of 272,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 272 are 1, 2, 4, 8, 16, 17, 34, 68, 136, 272
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 272,420 is 4.
Lets's calculate GCF of 272,420
| 2 | 272, 420 |
| 2 | 136, 210 |
| 68, 105 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 272,420 By Matching Biggest Common Factor Method
Now, list down the factors of 272
:1,2,4,8,16,17,34,68,136,272
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 272,420 . The biggest common factor number is the GCF number.
So the greatest common factor 272,420 is 4.
Lets's calculate LCM of 77,359
Given numbers has no common factors except 1. So, there LCM is their product i.e 27643
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/27643
Therefore, the GCF of Fractions 272/77,420/359 is 4/27643
Least Common Multiple of 77,359 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 77,359 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(77,359) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(77,359) x common factors =1 x 1 = 1
LCM(77,359) = ( 77 × 359 ) / 1
LCM(77,359) = 27643 / 1
LCM(77,359) = 27643
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FAQs on GCF of Fractions of 272/77, 420/359
1. What is the HCF of 272,420?
The HCF of 272,420 is 4
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 272/77, 420/359?
Answer: GCF of Numerators as per given numbers 272/77, 420/359 is
GCF of Numerators i.e. for 272,420 is 4
LCM of denominators i.e. for 77,359 is 27643.
Thus, GCF of Fractions is 4/27643.Finally, GCF of Fractions for 272/77, 420/359 is 4/27643.