GCF of 840/52, 400/711
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 840/52, 400/711 i.e 40/36972 easily. The following is the detailed procedure to determine the greatest common factor of fractions 840/52, 400/711.
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 840/52,400/711?
Given fractions are 840/52,400/711
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 840/52,400/711, numerators are 840,400
Denominators are 52,711
The GCF of 840,400 is 40 .
LCM of 52,711 is 36972.
The greatest common factor of 840/52,400/711 = [GCF of 840,400]/[LCM of 52,711]= 40/36972
Therefore, the GCF of 840/52,400/711 is 40/36972.
To find the highest common factor of 840,400, we have to find the factors of both numbers and list the highest common factor.
The factors of 840 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840
The factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
The HCF of 840,400 is 40.
Lets's calculate GCF of 840,400
| 2 | 840, 400 |
| 2 | 420, 200 |
| 2 | 210, 100 |
| 5 | 105, 50 |
| 21, 10 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 5 = 40
Greatest Common Factor of 840,400 By Matching Biggest Common Factor Method
Now, list down the factors of 840
:1,2,3,4,5,6,7,8,10,12,14,15,20,21,24,28,30,35,40,42,56,60,70,84,105,120,140,168,210,280,420,840
Now, list down the factors of 400
:1,2,4,5,8,10,16,20,25,40,50,80,100,200,400
Greatest Common Factor
We found the factors 840,400 . The biggest common factor number is the GCF number.
So the greatest common factor 840,400 is 40.
Lets's calculate LCM of 52,711
Given numbers has no common factors except 1. So, there LCM is their product i.e 36972
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 40/36972
Therefore, the GCF of Fractions 840/52,400/711 is 40/36972
Least Common Multiple of 52,711 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 52,711 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(52,711) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(52,711) x common factors =1 x 1 = 1
LCM(52,711) = ( 52 × 711 ) / 1
LCM(52,711) = 36972 / 1
LCM(52,711) = 36972
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FAQs on GCF of Fractions of 840/52, 400/711
1. What is the HCF of 840,400?
The HCF of 840,400 is 40
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 840/52, 400/711?
Answer: GCF of Numerators as per given numbers 840/52, 400/711 is
GCF of Numerators i.e. for 840,400 is 40
LCM of denominators i.e. for 52,711 is 36972.
Thus, GCF of Fractions is 40/36972.Finally, GCF of Fractions for 840/52, 400/711 is 40/36972.