GCF of 710/82, 780/567
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 710/82, 780/567 i.e 10/46494 easily. The following is the detailed procedure to determine the greatest common factor of fractions 710/82, 780/567.
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 710/82,780/567?
Given fractions are 710/82,780/567
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 710/82,780/567, numerators are 710,780
Denominators are 82,567
The GCF of 710,780 is 10 .
LCM of 82,567 is 46494.
The greatest common factor of 710/82,780/567 = [GCF of 710,780]/[LCM of 82,567]= 10/46494
Therefore, the GCF of 710/82,780/567 is 10/46494.
To find the highest common factor of 710,780, we have to find the factors of both numbers and list the highest common factor.
The factors of 710 are 1, 2, 5, 10, 71, 142, 355, 710
The factors of 780 are 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390, 780
The HCF of 710,780 is 10.
Lets's calculate GCF of 710,780
| 2 | 710, 780 |
| 5 | 355, 390 |
| 71, 78 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 710,780 By Matching Biggest Common Factor Method
Now, list down the factors of 710
:1,2,5,10,71,142,355,710
Now, list down the factors of 780
:1,2,3,4,5,6,10,12,13,15,20,26,30,39,52,60,65,78,130,156,195,260,390,780
Greatest Common Factor
We found the factors 710,780 . The biggest common factor number is the GCF number.
So the greatest common factor 710,780 is 10.
Lets's calculate LCM of 82,567
Given numbers has no common factors except 1. So, there LCM is their product i.e 46494
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/46494
Therefore, the GCF of Fractions 710/82,780/567 is 10/46494
Least Common Multiple of 82,567 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 82,567 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(82,567) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(82,567) x common factors =1 x 1 = 1
LCM(82,567) = ( 82 × 567 ) / 1
LCM(82,567) = 46494 / 1
LCM(82,567) = 46494
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FAQs on GCF of Fractions of 710/82, 780/567
1. What is the HCF of 710,780?
The HCF of 710,780 is 10
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 710/82, 780/567?
Answer: GCF of Numerators as per given numbers 710/82, 780/567 is
GCF of Numerators i.e. for 710,780 is 10
LCM of denominators i.e. for 82,567 is 46494.
Thus, GCF of Fractions is 10/46494.Finally, GCF of Fractions for 710/82, 780/567 is 10/46494.