GCF of 752/540, 416/698
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 752/540, 416/698 i.e 16/188460 easily. The following is the detailed procedure to determine the greatest common factor of fractions 752/540, 416/698.
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 752/540,416/698?
Given fractions are 752/540,416/698
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 752/540,416/698, numerators are 752,416
Denominators are 540,698
The GCF of 752,416 is 16 .
LCM of 540,698 is 188460.
The greatest common factor of 752/540,416/698 = [GCF of 752,416]/[LCM of 540,698]= 16/188460
Therefore, the GCF of 752/540,416/698 is 16/188460.
To find the highest common factor of 752,416, we have to find the factors of both numbers and list the highest common factor.
The factors of 752 are 1, 2, 4, 8, 16, 47, 94, 188, 376, 752
The factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416
The HCF of 752,416 is 16.
Lets's calculate GCF of 752,416
| 2 | 752, 416 |
| 2 | 376, 208 |
| 2 | 188, 104 |
| 2 | 94, 52 |
| 47, 26 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16
Greatest Common Factor of 752,416 By Matching Biggest Common Factor Method
Now, list down the factors of 752
:1,2,4,8,16,47,94,188,376,752
Now, list down the factors of 416
:1,2,4,8,13,16,26,32,52,104,208,416
Greatest Common Factor
We found the factors 752,416 . The biggest common factor number is the GCF number.
So the greatest common factor 752,416 is 16.
Lets's calculate LCM of 540,698
| 2 | 540, 698 |
| 270, 349 |
∴ So the LCM of the given numbers is 2 x 270 x 349 = 188460
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/188460
Therefore, the GCF of Fractions 752/540,416/698 is 16/188460
Least Common Multiple of 540,698 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 540,698 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(540,698) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(540,698) x common factors =2 x 1 = 2
LCM(540,698) = ( 540 × 698 ) / 2
LCM(540,698) = 376920 / 2
LCM(540,698) = 188460
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FAQs on GCF of Fractions of 752/540, 416/698
1. What is the HCF of 752,416?
The HCF of 752,416 is 16
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 752/540, 416/698?
Answer: GCF of Numerators as per given numbers 752/540, 416/698 is
GCF of Numerators i.e. for 752,416 is 16
LCM of denominators i.e. for 540,698 is 188460.
Thus, GCF of Fractions is 16/188460.Finally, GCF of Fractions for 752/540, 416/698 is 16/188460.