GCF of 61/286, 80/172, 470/762
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 61/286, 80/172, 470/762 i.e 1/9371076 easily. The following is the detailed procedure to determine the greatest common factor of fractions 61/286, 80/172, 470/762.
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 61/286,80/172,470/762?
Given fractions are 61/286,80/172,470/762
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 61/286,80/172,470/762, numerators are 61,80,470
Denominators are 286,172,762
The GCF of 61,80,470 is 1 .
LCM of 286,172,762 is 9371076.
The greatest common factor of 61/286,80/172,470/762 = [GCF of 61,80,470]/[LCM of 286,172,762]= 1/9371076
Therefore, the GCF of 61/286,80/172,470/762 is 1/9371076.
To find the highest common factor of 61,80,470, we have to find the factors of both numbers and list the highest common factor.
The factors of 61 are 1, 61
The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
The factors of 470 are 1, 2, 5, 10, 47, 94, 235, 470
The HCF of 61,80,470 is 1.
Lets's calculate GCF of 61,80,470
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 61,80,470 By Matching Biggest Common Factor Method
Now, list down the factors of 61
:1,61
Now, list down the factors of 80
:1,2,4,5,8,10,16,20,40,80
Now, list down the factors of 470
:1,2,5,10,47,94,235,470
Greatest Common Factor
We found the factors 61,80,470 . The biggest common factor number is the GCF number.
So the greatest common factor 61,80,470 is 1.
Lets's calculate LCM of 286,172,762
| 2 | 286, 172, 762 |
| 143, 86, 381 |
∴ So the LCM of the given numbers is 2 x 143 x 86 x 381 = 9371076
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/9371076
Therefore, the GCF of Fractions 61/286,80/172,470/762 is 1/9371076
Least Common Multiple of 286,172,762 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 286,172,762 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(286,172,762) = 2
common factors(in case of two or more numbers have common factors) = 2
GCF(286,172,762) x common factors =2 x 2 = 4
LCM(286,172,762) = ( 286 × 172 × 762 ) / 4
LCM(286,172,762) = 37484304 / 4
LCM(286,172,762) = 9371076
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FAQs on GCF of Fractions of 61/286, 80/172, 470/762
1. What is the HCF of 61,80,470?
The HCF of 61,80,470 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 61/286, 80/172, 470/762?
Answer: GCF of Numerators as per given numbers 61/286, 80/172, 470/762 is
GCF of Numerators i.e. for 61,80,470 is 1
LCM of denominators i.e. for 286,172,762 is 9371076.
Thus, GCF of Fractions is 1/9371076.Finally, GCF of Fractions for 61/286, 80/172, 470/762 is 1/9371076.