GCF of 966/987, 420/735
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 966/987, 420/735 i.e 42/34545 easily. The following is the detailed procedure to determine the greatest common factor of fractions 966/987, 420/735.
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 966/987,420/735?
Given fractions are 966/987,420/735
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 966/987,420/735, numerators are 966,420
Denominators are 987,735
The GCF of 966,420 is 42 .
LCM of 987,735 is 34545.
The greatest common factor of 966/987,420/735 = [GCF of 966,420]/[LCM of 987,735]= 42/34545
Therefore, the GCF of 966/987,420/735 is 42/34545.
To find the highest common factor of 966,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 966 are 1, 2, 3, 6, 7, 14, 21, 23, 42, 46, 69, 138, 161, 322, 483, 966
The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
The HCF of 966,420 is 42.
Lets's calculate GCF of 966,420
| 2 | 966, 420 |
| 3 | 483, 210 |
| 7 | 161, 70 |
| 23, 10 |
∴ So the GCF of the given numbers is 2 x 3 x 7 = 42
Greatest Common Factor of 966,420 By Matching Biggest Common Factor Method
Now, list down the factors of 966
:1,2,3,6,7,14,21,23,42,46,69,138,161,322,483,966
Now, list down the factors of 420
:1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Greatest Common Factor
We found the factors 966,420 . The biggest common factor number is the GCF number.
So the greatest common factor 966,420 is 42.
Lets's calculate LCM of 987,735
| 3 | 987, 735 |
| 7 | 329, 245 |
| 47, 35 |
∴ So the LCM of the given numbers is 3 x 7 x 47 x 35 = 34545
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 42/34545
Therefore, the GCF of Fractions 966/987,420/735 is 42/34545
Least Common Multiple of 987,735 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 987,735 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(987,735) = 21
common factors(in case of two or more numbers have common factors) = 1
GCF(987,735) x common factors =21 x 1 = 21
LCM(987,735) = ( 987 × 735 ) / 21
LCM(987,735) = 725445 / 21
LCM(987,735) = 34545
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FAQs on GCF of Fractions of 966/987, 420/735
1. What is the HCF of 966,420?
The HCF of 966,420 is 42
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 966/987, 420/735?
Answer: GCF of Numerators as per given numbers 966/987, 420/735 is
GCF of Numerators i.e. for 966,420 is 42
LCM of denominators i.e. for 987,735 is 34545.
Thus, GCF of Fractions is 42/34545.Finally, GCF of Fractions for 966/987, 420/735 is 42/34545.