GCF of 812/32, 870/572
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 812/32, 870/572 i.e 58/4576 easily. The following is the detailed procedure to determine the greatest common factor of fractions 812/32, 870/572.
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 812/32,870/572?
Given fractions are 812/32,870/572
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 812/32,870/572, numerators are 812,870
Denominators are 32,572
The GCF of 812,870 is 58 .
LCM of 32,572 is 4576.
The greatest common factor of 812/32,870/572 = [GCF of 812,870]/[LCM of 32,572]= 58/4576
Therefore, the GCF of 812/32,870/572 is 58/4576.
To find the highest common factor of 812,870, we have to find the factors of both numbers and list the highest common factor.
The factors of 812 are 1, 2, 4, 7, 14, 28, 29, 58, 116, 203, 406, 812
The factors of 870 are 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870
The HCF of 812,870 is 58.
Lets's calculate GCF of 812,870
| 2 | 812, 870 |
| 29 | 406, 435 |
| 14, 15 |
∴ So the GCF of the given numbers is 2 x 29 = 58
Greatest Common Factor of 812,870 By Matching Biggest Common Factor Method
Now, list down the factors of 812
:1,2,4,7,14,28,29,58,116,203,406,812
Now, list down the factors of 870
:1,2,3,5,6,10,15,29,30,58,87,145,174,290,435,870
Greatest Common Factor
We found the factors 812,870 . The biggest common factor number is the GCF number.
So the greatest common factor 812,870 is 58.
Lets's calculate LCM of 32,572
| 2 | 32, 572 |
| 2 | 16, 286 |
| 8, 143 |
∴ So the LCM of the given numbers is 2 x 2 x 8 x 143 = 4576
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 58/4576
Therefore, the GCF of Fractions 812/32,870/572 is 58/4576
Least Common Multiple of 32,572 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 32,572 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(32,572) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(32,572) x common factors =4 x 1 = 4
LCM(32,572) = ( 32 × 572 ) / 4
LCM(32,572) = 18304 / 4
LCM(32,572) = 4576
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 812/32, 870/572
1. What is the HCF of 812,870?
The HCF of 812,870 is 58
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 812/32, 870/572?
Answer: GCF of Numerators as per given numbers 812/32, 870/572 is
GCF of Numerators i.e. for 812,870 is 58
LCM of denominators i.e. for 32,572 is 4576.
Thus, GCF of Fractions is 58/4576.Finally, GCF of Fractions for 812/32, 870/572 is 58/4576.