GCF of 748/450, 408/638
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 748/450, 408/638 i.e 68/143550 easily. The following is the detailed procedure to determine the greatest common factor of fractions 748/450, 408/638.
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 748/450,408/638?
Given fractions are 748/450,408/638
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 748/450,408/638, numerators are 748,408
Denominators are 450,638
The GCF of 748,408 is 68 .
LCM of 450,638 is 143550.
The greatest common factor of 748/450,408/638 = [GCF of 748,408]/[LCM of 450,638]= 68/143550
Therefore, the GCF of 748/450,408/638 is 68/143550.
To find the highest common factor of 748,408, we have to find the factors of both numbers and list the highest common factor.
The factors of 748 are 1, 2, 4, 11, 17, 22, 34, 44, 68, 187, 374, 748
The factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408
The HCF of 748,408 is 68.
Lets's calculate GCF of 748,408
| 2 | 748, 408 |
| 2 | 374, 204 |
| 17 | 187, 102 |
| 11, 6 |
∴ So the GCF of the given numbers is 2 x 2 x 17 = 68
Greatest Common Factor of 748,408 By Matching Biggest Common Factor Method
Now, list down the factors of 748
:1,2,4,11,17,22,34,44,68,187,374,748
Now, list down the factors of 408
:1,2,3,4,6,8,12,17,24,34,51,68,102,136,204,408
Greatest Common Factor
We found the factors 748,408 . The biggest common factor number is the GCF number.
So the greatest common factor 748,408 is 68.
Lets's calculate LCM of 450,638
| 2 | 450, 638 |
| 225, 319 |
∴ So the LCM of the given numbers is 2 x 225 x 319 = 143550
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 68/143550
Therefore, the GCF of Fractions 748/450,408/638 is 68/143550
Least Common Multiple of 450,638 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 450,638 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(450,638) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(450,638) x common factors =2 x 1 = 2
LCM(450,638) = ( 450 × 638 ) / 2
LCM(450,638) = 287100 / 2
LCM(450,638) = 143550
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FAQs on GCF of Fractions of 748/450, 408/638
1. What is the HCF of 748,408?
The HCF of 748,408 is 68
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 748/450, 408/638?
Answer: GCF of Numerators as per given numbers 748/450, 408/638 is
GCF of Numerators i.e. for 748,408 is 68
LCM of denominators i.e. for 450,638 is 143550.
Thus, GCF of Fractions is 68/143550.Finally, GCF of Fractions for 748/450, 408/638 is 68/143550.