GCF of 630/38, 675/410
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 630/38, 675/410 i.e 45/7790 easily. The following is the detailed procedure to determine the greatest common factor of fractions 630/38, 675/410.
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 630/38,675/410?
Given fractions are 630/38,675/410
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 630/38,675/410, numerators are 630,675
Denominators are 38,410
The GCF of 630,675 is 45 .
LCM of 38,410 is 7790.
The greatest common factor of 630/38,675/410 = [GCF of 630,675]/[LCM of 38,410]= 45/7790
Therefore, the GCF of 630/38,675/410 is 45/7790.
To find the highest common factor of 630,675, we have to find the factors of both numbers and list the highest common factor.
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 factors of 675 are 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675
The HCF of 630,675 is 45.
Lets's calculate GCF of 630,675
| 3 | 630, 675 |
| 3 | 210, 225 |
| 5 | 70, 75 |
| 14, 15 |
∴ So the GCF of the given numbers is 3 x 3 x 5 = 45
Greatest Common Factor of 630,675 By Matching Biggest Common Factor Method
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
Now, list down the factors of 675
:1,3,5,9,15,25,27,45,75,135,225,675
Greatest Common Factor
We found the factors 630,675 . The biggest common factor number is the GCF number.
So the greatest common factor 630,675 is 45.
Lets's calculate LCM of 38,410
| 2 | 38, 410 |
| 19, 205 |
∴ So the LCM of the given numbers is 2 x 19 x 205 = 7790
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 45/7790
Therefore, the GCF of Fractions 630/38,675/410 is 45/7790
Least Common Multiple of 38,410 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 38,410 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(38,410) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(38,410) x common factors =2 x 1 = 2
LCM(38,410) = ( 38 × 410 ) / 2
LCM(38,410) = 15580 / 2
LCM(38,410) = 7790
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FAQs on GCF of Fractions of 630/38, 675/410
1. What is the HCF of 630,675?
The HCF of 630,675 is 45
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 630/38, 675/410?
Answer: GCF of Numerators as per given numbers 630/38, 675/410 is
GCF of Numerators i.e. for 630,675 is 45
LCM of denominators i.e. for 38,410 is 7790.
Thus, GCF of Fractions is 45/7790.Finally, GCF of Fractions for 630/38, 675/410 is 45/7790.