GCF of 490/1600, 630/2560
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 490/1600, 630/2560 i.e 70/12800 easily. The following is the detailed procedure to determine the greatest common factor of fractions 490/1600, 630/2560.
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 490/1600,630/2560?
Given fractions are 490/1600,630/2560
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 490/1600,630/2560, numerators are 490,630
Denominators are 1600,2560
The GCF of 490,630 is 70 .
LCM of 1600,2560 is 12800.
The greatest common factor of 490/1600,630/2560 = [GCF of 490,630]/[LCM of 1600,2560]= 70/12800
Therefore, the GCF of 490/1600,630/2560 is 70/12800.
To find the highest common factor of 490,630, we have to find the factors of both numbers and list the highest common factor.
The factors of 490 are 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 490
The factors of 630 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, 630
The HCF of 490,630 is 70.
Lets's calculate GCF of 490,630
| 2 | 490, 630 |
| 5 | 245, 315 |
| 7 | 49, 63 |
| 7, 9 |
∴ So the GCF of the given numbers is 2 x 5 x 7 = 70
Greatest Common Factor of 490,630 By Matching Biggest Common Factor Method
Now, list down the factors of 490
:1,2,5,7,10,14,35,49,70,98,245,490
Now, list down the factors of 630
:1,2,3,5,6,7,9,10,14,15,18,21,30,35,42,45,63,70,90,105,126,210,315,630
Greatest Common Factor
We found the factors 490,630 . The biggest common factor number is the GCF number.
So the greatest common factor 490,630 is 70.
Lets's calculate LCM of 1600,2560
| 2 | 1600, 2560 |
| 2 | 800, 1280 |
| 2 | 400, 640 |
| 2 | 200, 320 |
| 2 | 100, 160 |
| 2 | 50, 80 |
| 5 | 25, 40 |
| 5, 8 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 8 = 12800
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 70/12800
Therefore, the GCF of Fractions 490/1600,630/2560 is 70/12800
Least Common Multiple of 1600,2560 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 1600,2560 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(1600,2560) = 320
common factors(in case of two or more numbers have common factors) = 1
GCF(1600,2560) x common factors =320 x 1 = 320
LCM(1600,2560) = ( 1600 × 2560 ) / 320
LCM(1600,2560) = 4096000 / 320
LCM(1600,2560) = 12800
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FAQs on GCF of Fractions of 490/1600, 630/2560
1. What is the HCF of 490,630?
The HCF of 490,630 is 70
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 490/1600, 630/2560?
Answer: GCF of Numerators as per given numbers 490/1600, 630/2560 is
GCF of Numerators i.e. for 490,630 is 70
LCM of denominators i.e. for 1600,2560 is 12800.
Thus, GCF of Fractions is 70/12800.Finally, GCF of Fractions for 490/1600, 630/2560 is 70/12800.