GCF of 7560/967, 8460/720
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7560/967, 8460/720 i.e 180/696240 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7560/967, 8460/720.
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 7560/967,8460/720?
Given fractions are 7560/967,8460/720
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 7560/967,8460/720, numerators are 7560,8460
Denominators are 967,720
The GCF of 7560,8460 is 180 .
LCM of 967,720 is 696240.
The greatest common factor of 7560/967,8460/720 = [GCF of 7560,8460]/[LCM of 967,720]= 180/696240
Therefore, the GCF of 7560/967,8460/720 is 180/696240.
To find the highest common factor of 7560,8460, we have to find the factors of both numbers and list the highest common factor.
The factors of 7560 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 27, 28, 30, 35, 36, 40, 42, 45, 54, 56, 60, 63, 70, 72, 84, 90, 105, 108, 120, 126, 135, 140, 168, 180, 189, 210, 216, 252, 270, 280, 315, 360, 378, 420, 504, 540, 630, 756, 840, 945, 1080, 1260, 1512, 1890, 2520, 3780, 7560
The factors of 8460 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 47, 60, 90, 94, 141, 180, 188, 235, 282, 423, 470, 564, 705, 846, 940, 1410, 1692, 2115, 2820, 4230, 8460
The HCF of 7560,8460 is 180.
Lets's calculate GCF of 7560,8460
| 2 | 7560, 8460 |
| 2 | 3780, 4230 |
| 3 | 1890, 2115 |
| 3 | 630, 705 |
| 5 | 210, 235 |
| 42, 47 |
∴ So the GCF of the given numbers is 2 x 2 x 3 x 3 x 5 = 180
Greatest Common Factor of 7560,8460 By Matching Biggest Common Factor Method
Now, list down the factors of 7560
:1,2,3,4,5,6,7,8,9,10,12,14,15,18,20,21,24,27,28,30,35,36,40,42,45,54,56,60,63,70,72,84,90,105,108,120,126,135,140,168,180,189,210,216,252,270,280,315,360,378,420,504,540,630,756,840,945,1080,1260,1512,1890,2520,3780,7560
Now, list down the factors of 8460
:1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,47,60,90,94,141,180,188,235,282,423,470,564,705,846,940,1410,1692,2115,2820,4230,8460
Greatest Common Factor
We found the factors 7560,8460 . The biggest common factor number is the GCF number.
So the greatest common factor 7560,8460 is 180.
Lets's calculate LCM of 967,720
Given numbers has no common factors except 1. So, there LCM is their product i.e 696240
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 180/696240
Therefore, the GCF of Fractions 7560/967,8460/720 is 180/696240
Least Common Multiple of 967,720 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 967,720 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(967,720) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(967,720) x common factors =1 x 1 = 1
LCM(967,720) = ( 967 × 720 ) / 1
LCM(967,720) = 696240 / 1
LCM(967,720) = 696240
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FAQs on GCF of Fractions of 7560/967, 8460/720
1. What is the HCF of 7560,8460?
The HCF of 7560,8460 is 180
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 7560/967, 8460/720?
Answer: GCF of Numerators as per given numbers 7560/967, 8460/720 is
GCF of Numerators i.e. for 7560,8460 is 180
LCM of denominators i.e. for 967,720 is 696240.
Thus, GCF of Fractions is 180/696240.Finally, GCF of Fractions for 7560/967, 8460/720 is 180/696240.