GCF of 720/92, 420/177
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 720/92, 420/177 i.e 60/16284 easily. The following is the detailed procedure to determine the greatest common factor of fractions 720/92, 420/177.
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 720/92,420/177?
Given fractions are 720/92,420/177
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 720/92,420/177, numerators are 720,420
Denominators are 92,177
The GCF of 720,420 is 60 .
LCM of 92,177 is 16284.
The greatest common factor of 720/92,420/177 = [GCF of 720,420]/[LCM of 92,177]= 60/16284
Therefore, the GCF of 720/92,420/177 is 60/16284.
To find the highest common factor of 720,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 720 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720
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 720,420 is 60.
Lets's calculate GCF of 720,420
| 2 | 720, 420 |
| 2 | 360, 210 |
| 3 | 180, 105 |
| 5 | 60, 35 |
| 12, 7 |
∴ So the GCF of the given numbers is 2 x 2 x 3 x 5 = 60
Greatest Common Factor of 720,420 By Matching Biggest Common Factor Method
Now, list down the factors of 720
:1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,30,36,40,45,48,60,72,80,90,120,144,180,240,360,720
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 720,420 . The biggest common factor number is the GCF number.
So the greatest common factor 720,420 is 60.
Lets's calculate LCM of 92,177
Given numbers has no common factors except 1. So, there LCM is their product i.e 16284
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 60/16284
Therefore, the GCF of Fractions 720/92,420/177 is 60/16284
Least Common Multiple of 92,177 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 92,177 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(92,177) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(92,177) x common factors =1 x 1 = 1
LCM(92,177) = ( 92 × 177 ) / 1
LCM(92,177) = 16284 / 1
LCM(92,177) = 16284
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FAQs on GCF of Fractions of 720/92, 420/177
1. What is the HCF of 720,420?
The HCF of 720,420 is 60
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 720/92, 420/177?
Answer: GCF of Numerators as per given numbers 720/92, 420/177 is
GCF of Numerators i.e. for 720,420 is 60
LCM of denominators i.e. for 92,177 is 16284.
Thus, GCF of Fractions is 60/16284.Finally, GCF of Fractions for 720/92, 420/177 is 60/16284.