GCF of 977/40, 978/69, 685/32
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 977/40, 978/69, 685/32 i.e 1/11040 easily. The following is the detailed procedure to determine the greatest common factor of fractions 977/40, 978/69, 685/32.
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 977/40,978/69,685/32?
Given fractions are 977/40,978/69,685/32
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 977/40,978/69,685/32, numerators are 977,978,685
Denominators are 40,69,32
The GCF of 977,978,685 is 1 .
LCM of 40,69,32 is 11040.
The greatest common factor of 977/40,978/69,685/32 = [GCF of 977,978,685]/[LCM of 40,69,32]= 1/11040
Therefore, the GCF of 977/40,978/69,685/32 is 1/11040.
To find the highest common factor of 977,978,685, we have to find the factors of both numbers and list the highest common factor.
The factors of 977 are 1, 977
The factors of 978 are 1, 2, 3, 6, 163, 326, 489, 978
The factors of 685 are 1, 5, 137, 685
The HCF of 977,978,685 is 1.
Lets's calculate GCF of 977,978,685
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 977,978,685 By Matching Biggest Common Factor Method
Now, list down the factors of 977
:1,977
Now, list down the factors of 978
:1,2,3,6,163,326,489,978
Now, list down the factors of 685
:1,5,137,685
Greatest Common Factor
We found the factors 977,978,685 . The biggest common factor number is the GCF number.
So the greatest common factor 977,978,685 is 1.
Lets's calculate LCM of 40,69,32
| 2 | 40, 69, 32 |
| 2 | 20, 69, 16 |
| 2 | 10, 69, 8 |
| 5, 69, 4 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 5 x 69 x 4 = 11040
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/11040
Therefore, the GCF of Fractions 977/40,978/69,685/32 is 1/11040
Least Common Multiple of 40,69,32 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 40,69,32 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(40,69,32) = 1
common factors(in case of two or more numbers have common factors) = 8
GCF(40,69,32) x common factors =1 x 8 = 8
LCM(40,69,32) = ( 40 × 69 × 32 ) / 8
LCM(40,69,32) = 88320 / 8
LCM(40,69,32) = 11040
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FAQs on GCF of Fractions of 977/40, 978/69, 685/32
1. What is the HCF of 977,978,685?
The HCF of 977,978,685 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 977/40, 978/69, 685/32?
Answer: GCF of Numerators as per given numbers 977/40, 978/69, 685/32 is
GCF of Numerators i.e. for 977,978,685 is 1
LCM of denominators i.e. for 40,69,32 is 11040.
Thus, GCF of Fractions is 1/11040.Finally, GCF of Fractions for 977/40, 978/69, 685/32 is 1/11040.