GCF of 749/540, 1918/584
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 749/540, 1918/584 i.e 7/78840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 749/540, 1918/584.
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 749/540,1918/584?
Given fractions are 749/540,1918/584
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 749/540,1918/584, numerators are 749,1918
Denominators are 540,584
The GCF of 749,1918 is 7 .
LCM of 540,584 is 78840.
The greatest common factor of 749/540,1918/584 = [GCF of 749,1918]/[LCM of 540,584]= 7/78840
Therefore, the GCF of 749/540,1918/584 is 7/78840.
To find the highest common factor of 749,1918, we have to find the factors of both numbers and list the highest common factor.
The factors of 749 are 1, 7, 107, 749
The factors of 1918 are 1, 2, 7, 14, 137, 274, 959, 1918
The HCF of 749,1918 is 7.
Lets's calculate GCF of 749,1918
| 7 | 749, 1918 |
| 107, 274 |
∴ So the GCF of the given numbers is 7 = 7
Greatest Common Factor of 749,1918 By Matching Biggest Common Factor Method
Now, list down the factors of 749
:1,7,107,749
Now, list down the factors of 1918
:1,2,7,14,137,274,959,1918
Greatest Common Factor
We found the factors 749,1918 . The biggest common factor number is the GCF number.
So the greatest common factor 749,1918 is 7.
Lets's calculate LCM of 540,584
| 2 | 540, 584 |
| 2 | 270, 292 |
| 135, 146 |
∴ So the LCM of the given numbers is 2 x 2 x 135 x 146 = 78840
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/78840
Therefore, the GCF of Fractions 749/540,1918/584 is 7/78840
Least Common Multiple of 540,584 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 540,584 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(540,584) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(540,584) x common factors =4 x 1 = 4
LCM(540,584) = ( 540 × 584 ) / 4
LCM(540,584) = 315360 / 4
LCM(540,584) = 78840
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FAQs on GCF of Fractions of 749/540, 1918/584
1. What is the HCF of 749,1918?
The HCF of 749,1918 is 7
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 749/540, 1918/584?
Answer: GCF of Numerators as per given numbers 749/540, 1918/584 is
GCF of Numerators i.e. for 749,1918 is 7
LCM of denominators i.e. for 540,584 is 78840.
Thus, GCF of Fractions is 7/78840.Finally, GCF of Fractions for 749/540, 1918/584 is 7/78840.