GCF of 276/456, 420/947
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 276/456, 420/947 i.e 12/431832 easily. The following is the detailed procedure to determine the greatest common factor of fractions 276/456, 420/947.
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 276/456,420/947?
Given fractions are 276/456,420/947
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 276/456,420/947, numerators are 276,420
Denominators are 456,947
The GCF of 276,420 is 12 .
LCM of 456,947 is 431832.
The greatest common factor of 276/456,420/947 = [GCF of 276,420]/[LCM of 456,947]= 12/431832
Therefore, the GCF of 276/456,420/947 is 12/431832.
To find the highest common factor of 276,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 276 are 1, 2, 3, 4, 6, 12, 23, 46, 69, 92, 138, 276
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 276,420 is 12.
Lets's calculate GCF of 276,420
| 2 | 276, 420 |
| 2 | 138, 210 |
| 3 | 69, 105 |
| 23, 35 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Greatest Common Factor of 276,420 By Matching Biggest Common Factor Method
Now, list down the factors of 276
:1,2,3,4,6,12,23,46,69,92,138,276
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 276,420 . The biggest common factor number is the GCF number.
So the greatest common factor 276,420 is 12.
Lets's calculate LCM of 456,947
Given numbers has no common factors except 1. So, there LCM is their product i.e 431832
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/431832
Therefore, the GCF of Fractions 276/456,420/947 is 12/431832
Least Common Multiple of 456,947 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 456,947 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(456,947) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(456,947) x common factors =1 x 1 = 1
LCM(456,947) = ( 456 × 947 ) / 1
LCM(456,947) = 431832 / 1
LCM(456,947) = 431832
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FAQs on GCF of Fractions of 276/456, 420/947
1. What is the HCF of 276,420?
The HCF of 276,420 is 12
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 276/456, 420/947?
Answer: GCF of Numerators as per given numbers 276/456, 420/947 is
GCF of Numerators i.e. for 276,420 is 12
LCM of denominators i.e. for 456,947 is 431832.
Thus, GCF of Fractions is 12/431832.Finally, GCF of Fractions for 276/456, 420/947 is 12/431832.