Use our free GCF of Fractions Calculator tool to compute the GCF of 630/762, 267/454 i.e 3/172974 easily. The following is the detailed procedure to determine the greatest common factor of fractions 630/762, 267/454.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 630/762,267/454
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 630/762,267/454, numerators are 630,267
Denominators are 762,454
The GCF of 630,267 is 3 .
LCM of 762,454 is 172974.
The greatest common factor of 630/762,267/454 = [GCF of 630,267]/[LCM of 762,454]= 3/172974
Therefore, the GCF of 630/762,267/454 is 3/172974.
To find the highest common factor of 630,267, 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 267 are 1, 3, 89, 267
The HCF of 630,267 is 3.
Lets's calculate GCF of 630,267
3 | 630, 267 |
210, 89 |
∴ So the GCF of the given numbers is 3 = 3
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 267
:1,3,89,267
Greatest Common Factor
We found the factors 630,267 . The biggest common factor number is the GCF number.
So the greatest common factor 630,267 is 3.
Lets's calculate LCM of 762,454
2 | 762, 454 |
381, 227 |
∴ So the LCM of the given numbers is 2 x 381 x 227 = 172974
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/172974
Therefore, the GCF of Fractions 630/762,267/454 is 3/172974
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 762,454 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(762,454) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(762,454) x common factors =2 x 1 = 2
LCM(762,454) = ( 762 × 454 ) / 2
LCM(762,454) = 345948 / 2
LCM(762,454) = 172974
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 630,267?
The HCF of 630,267 is 3
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 630/762, 267/454?
Answer: GCF of Numerators as per given numbers 630/762, 267/454 is
GCF of Numerators i.e. for 630,267 is 3
LCM of denominators i.e. for 762,454 is 172974.
Thus, GCF of Fractions is 3/172974.Finally, GCF of Fractions for 630/762, 267/454 is 3/172974.