GCF of 1736/24, 7140/516
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1736/24, 7140/516 i.e 28/1032 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1736/24, 7140/516.
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 1736/24,7140/516?
Given fractions are 1736/24,7140/516
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 1736/24,7140/516, numerators are 1736,7140
Denominators are 24,516
The GCF of 1736,7140 is 28 .
LCM of 24,516 is 1032.
The greatest common factor of 1736/24,7140/516 = [GCF of 1736,7140]/[LCM of 24,516]= 28/1032
Therefore, the GCF of 1736/24,7140/516 is 28/1032.
To find the highest common factor of 1736,7140, we have to find the factors of both numbers and list the highest common factor.
The factors of 1736 are 1, 2, 4, 7, 8, 14, 28, 31, 56, 62, 124, 217, 248, 434, 868, 1736
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 1736,7140 is 28.
Lets's calculate GCF of 1736,7140
| 2 | 1736, 7140 |
| 2 | 868, 3570 |
| 7 | 434, 1785 |
| 62, 255 |
∴ So the GCF of the given numbers is 2 x 2 x 7 = 28
Greatest Common Factor of 1736,7140 By Matching Biggest Common Factor Method
Now, list down the factors of 1736
:1,2,4,7,8,14,28,31,56,62,124,217,248,434,868,1736
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 1736,7140 . The biggest common factor number is the GCF number.
So the greatest common factor 1736,7140 is 28.
Lets's calculate LCM of 24,516
| 2 | 24, 516 |
| 2 | 12, 258 |
| 3 | 6, 129 |
| 2, 43 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 2 x 43 = 1032
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 28/1032
Therefore, the GCF of Fractions 1736/24,7140/516 is 28/1032
Least Common Multiple of 24,516 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 24,516 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(24,516) = 12
common factors(in case of two or more numbers have common factors) = 1
GCF(24,516) x common factors =12 x 1 = 12
LCM(24,516) = ( 24 × 516 ) / 12
LCM(24,516) = 12384 / 12
LCM(24,516) = 1032
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FAQs on GCF of Fractions of 1736/24, 7140/516
1. What is the HCF of 1736,7140?
The HCF of 1736,7140 is 28
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 1736/24, 7140/516?
Answer: GCF of Numerators as per given numbers 1736/24, 7140/516 is
GCF of Numerators i.e. for 1736,7140 is 28
LCM of denominators i.e. for 24,516 is 1032.
Thus, GCF of Fractions is 28/1032.Finally, GCF of Fractions for 1736/24, 7140/516 is 28/1032.