GCF of 7584/244, 8514/680
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7584/244, 8514/680 i.e 6/41480 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7584/244, 8514/680.
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 7584/244,8514/680?
Given fractions are 7584/244,8514/680
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 7584/244,8514/680, numerators are 7584,8514
Denominators are 244,680
The GCF of 7584,8514 is 6 .
LCM of 244,680 is 41480.
The greatest common factor of 7584/244,8514/680 = [GCF of 7584,8514]/[LCM of 244,680]= 6/41480
Therefore, the GCF of 7584/244,8514/680 is 6/41480.
To find the highest common factor of 7584,8514, we have to find the factors of both numbers and list the highest common factor.
The factors of 7584 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 79, 96, 158, 237, 316, 474, 632, 948, 1264, 1896, 2528, 3792, 7584
The factors of 8514 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 43, 66, 86, 99, 129, 198, 258, 387, 473, 774, 946, 1419, 2838, 4257, 8514
The HCF of 7584,8514 is 6.
Lets's calculate GCF of 7584,8514
| 2 | 7584, 8514 |
| 3 | 3792, 4257 |
| 1264, 1419 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 7584,8514 By Matching Biggest Common Factor Method
Now, list down the factors of 7584
:1,2,3,4,6,8,12,16,24,32,48,79,96,158,237,316,474,632,948,1264,1896,2528,3792,7584
Now, list down the factors of 8514
:1,2,3,6,9,11,18,22,33,43,66,86,99,129,198,258,387,473,774,946,1419,2838,4257,8514
Greatest Common Factor
We found the factors 7584,8514 . The biggest common factor number is the GCF number.
So the greatest common factor 7584,8514 is 6.
Lets's calculate LCM of 244,680
| 2 | 244, 680 |
| 2 | 122, 340 |
| 61, 170 |
∴ So the LCM of the given numbers is 2 x 2 x 61 x 170 = 41480
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/41480
Therefore, the GCF of Fractions 7584/244,8514/680 is 6/41480
Least Common Multiple of 244,680 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 244,680 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(244,680) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(244,680) x common factors =4 x 1 = 4
LCM(244,680) = ( 244 × 680 ) / 4
LCM(244,680) = 165920 / 4
LCM(244,680) = 41480
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FAQs on GCF of Fractions of 7584/244, 8514/680
1. What is the HCF of 7584,8514?
The HCF of 7584,8514 is 6
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 7584/244, 8514/680?
Answer: GCF of Numerators as per given numbers 7584/244, 8514/680 is
GCF of Numerators i.e. for 7584,8514 is 6
LCM of denominators i.e. for 244,680 is 41480.
Thus, GCF of Fractions is 6/41480.Finally, GCF of Fractions for 7584/244, 8514/680 is 6/41480.