GCF of 53/70, 13/48, 420/75
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 53/70, 13/48, 420/75 i.e 1/8400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 53/70, 13/48, 420/75.
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 53/70,13/48,420/75?
Given fractions are 53/70,13/48,420/75
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 53/70,13/48,420/75, numerators are 53,13,420
Denominators are 70,48,75
The GCF of 53,13,420 is 1 .
LCM of 70,48,75 is 8400.
The greatest common factor of 53/70,13/48,420/75 = [GCF of 53,13,420]/[LCM of 70,48,75]= 1/8400
Therefore, the GCF of 53/70,13/48,420/75 is 1/8400.
To find the highest common factor of 53,13,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 53 are 1, 53
The factors of 13 are 1, 13
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 53,13,420 is 1.
Lets's calculate GCF of 53,13,420
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 53,13,420 By Matching Biggest Common Factor Method
Now, list down the factors of 53
:1,53
Now, list down the factors of 13
:1,13
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 53,13,420 . The biggest common factor number is the GCF number.
So the greatest common factor 53,13,420 is 1.
Lets's calculate LCM of 70,48,75
| 2 | 70, 48, 75 |
| 3 | 35, 24, 75 |
| 5 | 35, 8, 25 |
| 7, 8, 5 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 7 x 8 x 5 = 8400
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/8400
Therefore, the GCF of Fractions 53/70,13/48,420/75 is 1/8400
Least Common Multiple of 70,48,75 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 70,48,75 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(70,48,75) = 1
common factors(in case of two or more numbers have common factors) = 30
GCF(70,48,75) x common factors =1 x 30 = 30
LCM(70,48,75) = ( 70 × 48 × 75 ) / 30
LCM(70,48,75) = 252000 / 30
LCM(70,48,75) = 8400
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FAQs on GCF of Fractions of 53/70, 13/48, 420/75
1. What is the HCF of 53,13,420?
The HCF of 53,13,420 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 53/70, 13/48, 420/75?
Answer: GCF of Numerators as per given numbers 53/70, 13/48, 420/75 is
GCF of Numerators i.e. for 53,13,420 is 1
LCM of denominators i.e. for 70,48,75 is 8400.
Thus, GCF of Fractions is 1/8400.Finally, GCF of Fractions for 53/70, 13/48, 420/75 is 1/8400.