GCF of 5/56, 49/52, 62/468, 420/369
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5/56, 49/52, 62/468, 420/369 i.e 1/268632 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5/56, 49/52, 62/468, 420/369.
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 5/56,49/52,62/468,420/369?
Given fractions are 5/56,49/52,62/468,420/369
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 5/56,49/52,62/468,420/369, numerators are 5,49,62,420
Denominators are 56,52,468,369
The GCF of 5,49,62,420 is 1 .
LCM of 56,52,468,369 is 268632.
The greatest common factor of 5/56,49/52,62/468,420/369 = [GCF of 5,49,62,420]/[LCM of 56,52,468,369]= 1/268632
Therefore, the GCF of 5/56,49/52,62/468,420/369 is 1/268632.
To find the highest common factor of 5,49,62,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 5 are 1, 5
The factors of 49 are 1, 7, 49
The factors of 62 are 1, 2, 31, 62
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 5,49,62,420 is 1.
Lets's calculate GCF of 5,49,62,420
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 5,49,62,420 By Matching Biggest Common Factor Method
Now, list down the factors of 5
:1,5
Now, list down the factors of 49
:1,7,49
Now, list down the factors of 62
:1,2,31,62
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 5,49,62,420 . The biggest common factor number is the GCF number.
So the greatest common factor 5,49,62,420 is 1.
Lets's calculate LCM of 56,52,468,369
| 2 | 56, 52, 468, 369 |
| 2 | 28, 26, 234, 369 |
| 3 | 14, 13, 117, 369 |
| 3 | 14, 13, 39, 123 |
| 13 | 14, 13, 13, 41 |
| 14, 1, 1, 41 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 3 x 13 x 14 x 1 x 1 x 41 = 268632
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/268632
Therefore, the GCF of Fractions 5/56,49/52,62/468,420/369 is 1/268632
Least Common Multiple of 56,52,468,369 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 56,52,468,369 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(56,52,468,369) = 1
common factors(in case of two or more numbers have common factors) = 1872
GCF(56,52,468,369) x common factors =1 x 1872 = 1872
LCM(56,52,468,369) = ( 56 × 52 × 468 × 369 ) / 1872
LCM(56,52,468,369) = 502879104 / 1872
LCM(56,52,468,369) = 268632
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FAQs on GCF of Fractions of 5/56, 49/52, 62/468, 420/369
1. What is the HCF of 5,49,62,420?
The HCF of 5,49,62,420 is 1
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 5/56, 49/52, 62/468, 420/369?
Answer: GCF of Numerators as per given numbers 5/56, 49/52, 62/468, 420/369 is
GCF of Numerators i.e. for 5,49,62,420 is 1
LCM of denominators i.e. for 56,52,468,369 is 268632.
Thus, GCF of Fractions is 1/268632.Finally, GCF of Fractions for 5/56, 49/52, 62/468, 420/369 is 1/268632.