GCF of 924/500, 7140/824
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 924/500, 7140/824 i.e 84/103000 easily. The following is the detailed procedure to determine the greatest common factor of fractions 924/500, 7140/824.
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 924/500,7140/824?
Given fractions are 924/500,7140/824
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 924/500,7140/824, numerators are 924,7140
Denominators are 500,824
The GCF of 924,7140 is 84 .
LCM of 500,824 is 103000.
The greatest common factor of 924/500,7140/824 = [GCF of 924,7140]/[LCM of 500,824]= 84/103000
Therefore, the GCF of 924/500,7140/824 is 84/103000.
To find the highest common factor of 924,7140, we have to find the factors of both numbers and list the highest common factor.
The factors of 924 are 1, 2, 3, 4, 6, 7, 11, 12, 14, 21, 22, 28, 33, 42, 44, 66, 77, 84, 132, 154, 231, 308, 462, 924
The factors of 7140 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 17, 20, 21, 28, 30, 34, 35, 42, 51, 60, 68, 70, 84, 85, 102, 105, 119, 140, 170, 204, 210, 238, 255, 340, 357, 420, 476, 510, 595, 714, 1020, 1190, 1428, 1785, 2380, 3570, 7140
The HCF of 924,7140 is 84.
Lets's calculate GCF of 924,7140
| 2 | 924, 7140 |
| 2 | 462, 3570 |
| 3 | 231, 1785 |
| 7 | 77, 595 |
| 11, 85 |
∴ So the GCF of the given numbers is 2 x 2 x 3 x 7 = 84
Greatest Common Factor of 924,7140 By Matching Biggest Common Factor Method
Now, list down the factors of 924
:1,2,3,4,6,7,11,12,14,21,22,28,33,42,44,66,77,84,132,154,231,308,462,924
Now, list down the factors of 7140
:1,2,3,4,5,6,7,10,12,14,15,17,20,21,28,30,34,35,42,51,60,68,70,84,85,102,105,119,140,170,204,210,238,255,340,357,420,476,510,595,714,1020,1190,1428,1785,2380,3570,7140
Greatest Common Factor
We found the factors 924,7140 . The biggest common factor number is the GCF number.
So the greatest common factor 924,7140 is 84.
Lets's calculate LCM of 500,824
| 2 | 500, 824 |
| 2 | 250, 412 |
| 125, 206 |
∴ So the LCM of the given numbers is 2 x 2 x 125 x 206 = 103000
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 84/103000
Therefore, the GCF of Fractions 924/500,7140/824 is 84/103000
Least Common Multiple of 500,824 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 500,824 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(500,824) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(500,824) x common factors =4 x 1 = 4
LCM(500,824) = ( 500 × 824 ) / 4
LCM(500,824) = 412000 / 4
LCM(500,824) = 103000
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FAQs on GCF of Fractions of 924/500, 7140/824
1. What is the HCF of 924,7140?
The HCF of 924,7140 is 84
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 924/500, 7140/824?
Answer: GCF of Numerators as per given numbers 924/500, 7140/824 is
GCF of Numerators i.e. for 924,7140 is 84
LCM of denominators i.e. for 500,824 is 103000.
Thus, GCF of Fractions is 84/103000.Finally, GCF of Fractions for 924/500, 7140/824 is 84/103000.