GCF of 936/414, 360/766
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 936/414, 360/766 i.e 72/158562 easily. The following is the detailed procedure to determine the greatest common factor of fractions 936/414, 360/766.
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 936/414,360/766?
Given fractions are 936/414,360/766
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 936/414,360/766, numerators are 936,360
Denominators are 414,766
The GCF of 936,360 is 72 .
LCM of 414,766 is 158562.
The greatest common factor of 936/414,360/766 = [GCF of 936,360]/[LCM of 414,766]= 72/158562
Therefore, the GCF of 936/414,360/766 is 72/158562.
To find the highest common factor of 936,360, we have to find the factors of both numbers and list the highest common factor.
The factors of 936 are 1, 2, 3, 4, 6, 8, 9, 12, 13, 18, 24, 26, 36, 39, 52, 72, 78, 104, 117, 156, 234, 312, 468, 936
The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
The HCF of 936,360 is 72.
Lets's calculate GCF of 936,360
| 2 | 936, 360 |
| 2 | 468, 180 |
| 2 | 234, 90 |
| 3 | 117, 45 |
| 3 | 39, 15 |
| 13, 5 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 x 3 = 72
Greatest Common Factor of 936,360 By Matching Biggest Common Factor Method
Now, list down the factors of 936
:1,2,3,4,6,8,9,12,13,18,24,26,36,39,52,72,78,104,117,156,234,312,468,936
Now, list down the factors of 360
:1,2,3,4,5,6,8,9,10,12,15,18,20,24,30,36,40,45,60,72,90,120,180,360
Greatest Common Factor
We found the factors 936,360 . The biggest common factor number is the GCF number.
So the greatest common factor 936,360 is 72.
Lets's calculate LCM of 414,766
| 2 | 414, 766 |
| 207, 383 |
∴ So the LCM of the given numbers is 2 x 207 x 383 = 158562
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 72/158562
Therefore, the GCF of Fractions 936/414,360/766 is 72/158562
Least Common Multiple of 414,766 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 414,766 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,766) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(414,766) x common factors =2 x 1 = 2
LCM(414,766) = ( 414 × 766 ) / 2
LCM(414,766) = 317124 / 2
LCM(414,766) = 158562
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FAQs on GCF of Fractions of 936/414, 360/766
1. What is the HCF of 936,360?
The HCF of 936,360 is 72
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 936/414, 360/766?
Answer: GCF of Numerators as per given numbers 936/414, 360/766 is
GCF of Numerators i.e. for 936,360 is 72
LCM of denominators i.e. for 414,766 is 158562.
Thus, GCF of Fractions is 72/158562.Finally, GCF of Fractions for 936/414, 360/766 is 72/158562.