GCF of 3680/705, 1380/432
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3680/705, 1380/432 i.e 460/101520 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3680/705, 1380/432.
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 3680/705,1380/432?
Given fractions are 3680/705,1380/432
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 3680/705,1380/432, numerators are 3680,1380
Denominators are 705,432
The GCF of 3680,1380 is 460 .
LCM of 705,432 is 101520.
The greatest common factor of 3680/705,1380/432 = [GCF of 3680,1380]/[LCM of 705,432]= 460/101520
Therefore, the GCF of 3680/705,1380/432 is 460/101520.
To find the highest common factor of 3680,1380, we have to find the factors of both numbers and list the highest common factor.
The factors of 3680 are 1, 2, 4, 5, 8, 10, 16, 20, 23, 32, 40, 46, 80, 92, 115, 160, 184, 230, 368, 460, 736, 920, 1840, 3680
The factors of 1380 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 23, 30, 46, 60, 69, 92, 115, 138, 230, 276, 345, 460, 690, 1380
The HCF of 3680,1380 is 460.
Lets's calculate GCF of 3680,1380
| 2 | 3680, 1380 |
| 2 | 1840, 690 |
| 5 | 920, 345 |
| 23 | 184, 69 |
| 8, 3 |
∴ So the GCF of the given numbers is 2 x 2 x 5 x 23 = 460
Greatest Common Factor of 3680,1380 By Matching Biggest Common Factor Method
Now, list down the factors of 3680
:1,2,4,5,8,10,16,20,23,32,40,46,80,92,115,160,184,230,368,460,736,920,1840,3680
Now, list down the factors of 1380
:1,2,3,4,5,6,10,12,15,20,23,30,46,60,69,92,115,138,230,276,345,460,690,1380
Greatest Common Factor
We found the factors 3680,1380 . The biggest common factor number is the GCF number.
So the greatest common factor 3680,1380 is 460.
Lets's calculate LCM of 705,432
| 3 | 705, 432 |
| 235, 144 |
∴ So the LCM of the given numbers is 3 x 235 x 144 = 101520
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 460/101520
Therefore, the GCF of Fractions 3680/705,1380/432 is 460/101520
Least Common Multiple of 705,432 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 705,432 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(705,432) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(705,432) x common factors =3 x 1 = 3
LCM(705,432) = ( 705 × 432 ) / 3
LCM(705,432) = 304560 / 3
LCM(705,432) = 101520
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FAQs on GCF of Fractions of 3680/705, 1380/432
1. What is the HCF of 3680,1380?
The HCF of 3680,1380 is 460
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 3680/705, 1380/432?
Answer: GCF of Numerators as per given numbers 3680/705, 1380/432 is
GCF of Numerators i.e. for 3680,1380 is 460
LCM of denominators i.e. for 705,432 is 101520.
Thus, GCF of Fractions is 460/101520.Finally, GCF of Fractions for 3680/705, 1380/432 is 460/101520.