GCF of 7574/498, 7154/1567
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7574/498, 7154/1567 i.e 14/780366 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7574/498, 7154/1567.
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 7574/498,7154/1567?
Given fractions are 7574/498,7154/1567
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 7574/498,7154/1567, numerators are 7574,7154
Denominators are 498,1567
The GCF of 7574,7154 is 14 .
LCM of 498,1567 is 780366.
The greatest common factor of 7574/498,7154/1567 = [GCF of 7574,7154]/[LCM of 498,1567]= 14/780366
Therefore, the GCF of 7574/498,7154/1567 is 14/780366.
To find the highest common factor of 7574,7154, we have to find the factors of both numbers and list the highest common factor.
The factors of 7574 are 1, 2, 7, 14, 541, 1082, 3787, 7574
The factors of 7154 are 1, 2, 7, 14, 49, 73, 98, 146, 511, 1022, 3577, 7154
The HCF of 7574,7154 is 14.
Lets's calculate GCF of 7574,7154
| 2 | 7574, 7154 |
| 7 | 3787, 3577 |
| 541, 511 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 7574,7154 By Matching Biggest Common Factor Method
Now, list down the factors of 7574
:1,2,7,14,541,1082,3787,7574
Now, list down the factors of 7154
:1,2,7,14,49,73,98,146,511,1022,3577,7154
Greatest Common Factor
We found the factors 7574,7154 . The biggest common factor number is the GCF number.
So the greatest common factor 7574,7154 is 14.
Lets's calculate LCM of 498,1567
Given numbers has no common factors except 1. So, there LCM is their product i.e 780366
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/780366
Therefore, the GCF of Fractions 7574/498,7154/1567 is 14/780366
Least Common Multiple of 498,1567 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 498,1567 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(498,1567) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(498,1567) x common factors =1 x 1 = 1
LCM(498,1567) = ( 498 × 1567 ) / 1
LCM(498,1567) = 780366 / 1
LCM(498,1567) = 780366
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FAQs on GCF of Fractions of 7574/498, 7154/1567
1. What is the HCF of 7574,7154?
The HCF of 7574,7154 is 14
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 7574/498, 7154/1567?
Answer: GCF of Numerators as per given numbers 7574/498, 7154/1567 is
GCF of Numerators i.e. for 7574,7154 is 14
LCM of denominators i.e. for 498,1567 is 780366.
Thus, GCF of Fractions is 14/780366.Finally, GCF of Fractions for 7574/498, 7154/1567 is 14/780366.