GCF of 5460/743, 7560/3501
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5460/743, 7560/3501 i.e 420/2601243 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5460/743, 7560/3501.
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 5460/743,7560/3501?
Given fractions are 5460/743,7560/3501
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 5460/743,7560/3501, numerators are 5460,7560
Denominators are 743,3501
The GCF of 5460,7560 is 420 .
LCM of 743,3501 is 2601243.
The greatest common factor of 5460/743,7560/3501 = [GCF of 5460,7560]/[LCM of 743,3501]= 420/2601243
Therefore, the GCF of 5460/743,7560/3501 is 420/2601243.
To find the highest common factor of 5460,7560, we have to find the factors of both numbers and list the highest common factor.
The factors of 5460 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 13, 14, 15, 20, 21, 26, 28, 30, 35, 39, 42, 52, 60, 65, 70, 78, 84, 91, 105, 130, 140, 156, 182, 195, 210, 260, 273, 364, 390, 420, 455, 546, 780, 910, 1092, 1365, 1820, 2730, 5460
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 HCF of 5460,7560 is 420.
Lets's calculate GCF of 5460,7560
| 2 | 5460, 7560 |
| 2 | 2730, 3780 |
| 3 | 1365, 1890 |
| 5 | 455, 630 |
| 7 | 91, 126 |
| 13, 18 |
∴ So the GCF of the given numbers is 2 x 2 x 3 x 5 x 7 = 420
Greatest Common Factor of 5460,7560 By Matching Biggest Common Factor Method
Now, list down the factors of 5460
:1,2,3,4,5,6,7,10,12,13,14,15,20,21,26,28,30,35,39,42,52,60,65,70,78,84,91,105,130,140,156,182,195,210,260,273,364,390,420,455,546,780,910,1092,1365,1820,2730,5460
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
Greatest Common Factor
We found the factors 5460,7560 . The biggest common factor number is the GCF number.
So the greatest common factor 5460,7560 is 420.
Lets's calculate LCM of 743,3501
Given numbers has no common factors except 1. So, there LCM is their product i.e 2601243
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 420/2601243
Therefore, the GCF of Fractions 5460/743,7560/3501 is 420/2601243
Least Common Multiple of 743,3501 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 743,3501 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(743,3501) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(743,3501) x common factors =1 x 1 = 1
LCM(743,3501) = ( 743 × 3501 ) / 1
LCM(743,3501) = 2601243 / 1
LCM(743,3501) = 2601243
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FAQs on GCF of Fractions of 5460/743, 7560/3501
1. What is the HCF of 5460,7560?
The HCF of 5460,7560 is 420
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 5460/743, 7560/3501?
Answer: GCF of Numerators as per given numbers 5460/743, 7560/3501 is
GCF of Numerators i.e. for 5460,7560 is 420
LCM of denominators i.e. for 743,3501 is 2601243.
Thus, GCF of Fractions is 420/2601243.Finally, GCF of Fractions for 5460/743, 7560/3501 is 420/2601243.