GCF of 89/766, 84/261, 348/870
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 89/766, 84/261, 348/870 i.e 1/999630 easily. The following is the detailed procedure to determine the greatest common factor of fractions 89/766, 84/261, 348/870.
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 89/766,84/261,348/870?
Given fractions are 89/766,84/261,348/870
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 89/766,84/261,348/870, numerators are 89,84,348
Denominators are 766,261,870
The GCF of 89,84,348 is 1 .
LCM of 766,261,870 is 999630.
The greatest common factor of 89/766,84/261,348/870 = [GCF of 89,84,348]/[LCM of 766,261,870]= 1/999630
Therefore, the GCF of 89/766,84/261,348/870 is 1/999630.
To find the highest common factor of 89,84,348, we have to find the factors of both numbers and list the highest common factor.
The factors of 89 are 1, 89
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The factors of 348 are 1, 2, 3, 4, 6, 12, 29, 58, 87, 116, 174, 348
The HCF of 89,84,348 is 1.
Lets's calculate GCF of 89,84,348
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 89,84,348 By Matching Biggest Common Factor Method
Now, list down the factors of 89
:1,89
Now, list down the factors of 84
:1,2,3,4,6,7,12,14,21,28,42,84
Now, list down the factors of 348
:1,2,3,4,6,12,29,58,87,116,174,348
Greatest Common Factor
We found the factors 89,84,348 . The biggest common factor number is the GCF number.
So the greatest common factor 89,84,348 is 1.
Lets's calculate LCM of 766,261,870
| 2 | 766, 261, 870 |
| 3 | 383, 261, 435 |
| 29 | 383, 87, 145 |
| 383, 3, 5 |
∴ So the LCM of the given numbers is 2 x 3 x 29 x 383 x 3 x 5 = 999630
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/999630
Therefore, the GCF of Fractions 89/766,84/261,348/870 is 1/999630
Least Common Multiple of 766,261,870 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 766,261,870 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(766,261,870) = 1
common factors(in case of two or more numbers have common factors) = 174
GCF(766,261,870) x common factors =1 x 174 = 174
LCM(766,261,870) = ( 766 × 261 × 870 ) / 174
LCM(766,261,870) = 173935620 / 174
LCM(766,261,870) = 999630
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FAQs on GCF of Fractions of 89/766, 84/261, 348/870
1. What is the HCF of 89,84,348?
The HCF of 89,84,348 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 89/766, 84/261, 348/870?
Answer: GCF of Numerators as per given numbers 89/766, 84/261, 348/870 is
GCF of Numerators i.e. for 89,84,348 is 1
LCM of denominators i.e. for 766,261,870 is 999630.
Thus, GCF of Fractions is 1/999630.Finally, GCF of Fractions for 89/766, 84/261, 348/870 is 1/999630.