GCF of 970/78, 403/64, 810/84
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 970/78, 403/64, 810/84 i.e 1/17472 easily. The following is the detailed procedure to determine the greatest common factor of fractions 970/78, 403/64, 810/84.
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 970/78,403/64,810/84?
Given fractions are 970/78,403/64,810/84
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 970/78,403/64,810/84, numerators are 970,403,810
Denominators are 78,64,84
The GCF of 970,403,810 is 1 .
LCM of 78,64,84 is 17472.
The greatest common factor of 970/78,403/64,810/84 = [GCF of 970,403,810]/[LCM of 78,64,84]= 1/17472
Therefore, the GCF of 970/78,403/64,810/84 is 1/17472.
To find the highest common factor of 970,403,810, we have to find the factors of both numbers and list the highest common factor.
The factors of 970 are 1, 2, 5, 10, 97, 194, 485, 970
The factors of 403 are 1, 13, 31, 403
The factors of 810 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405, 810
The HCF of 970,403,810 is 1.
Lets's calculate GCF of 970,403,810
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 970,403,810 By Matching Biggest Common Factor Method
Now, list down the factors of 970
:1,2,5,10,97,194,485,970
Now, list down the factors of 403
:1,13,31,403
Now, list down the factors of 810
:1,2,3,5,6,9,10,15,18,27,30,45,54,81,90,135,162,270,405,810
Greatest Common Factor
We found the factors 970,403,810 . The biggest common factor number is the GCF number.
So the greatest common factor 970,403,810 is 1.
Lets's calculate LCM of 78,64,84
| 2 | 78, 64, 84 |
| 2 | 39, 32, 42 |
| 3 | 39, 16, 21 |
| 13, 16, 7 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 13 x 16 x 7 = 17472
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/17472
Therefore, the GCF of Fractions 970/78,403/64,810/84 is 1/17472
Least Common Multiple of 78,64,84 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 78,64,84 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(78,64,84) = 2
common factors(in case of two or more numbers have common factors) = 12
GCF(78,64,84) x common factors =2 x 12 = 24
LCM(78,64,84) = ( 78 × 64 × 84 ) / 24
LCM(78,64,84) = 419328 / 24
LCM(78,64,84) = 17472
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 970/78, 403/64, 810/84
1. What is the HCF of 970,403,810?
The HCF of 970,403,810 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 970/78, 403/64, 810/84?
Answer: GCF of Numerators as per given numbers 970/78, 403/64, 810/84 is
GCF of Numerators i.e. for 970,403,810 is 1
LCM of denominators i.e. for 78,64,84 is 17472.
Thus, GCF of Fractions is 1/17472.Finally, GCF of Fractions for 970/78, 403/64, 810/84 is 1/17472.