GCF of 532/68, 574/1509
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 532/68, 574/1509 i.e 14/102612 easily. The following is the detailed procedure to determine the greatest common factor of fractions 532/68, 574/1509.
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 532/68,574/1509?
Given fractions are 532/68,574/1509
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 532/68,574/1509, numerators are 532,574
Denominators are 68,1509
The GCF of 532,574 is 14 .
LCM of 68,1509 is 102612.
The greatest common factor of 532/68,574/1509 = [GCF of 532,574]/[LCM of 68,1509]= 14/102612
Therefore, the GCF of 532/68,574/1509 is 14/102612.
To find the highest common factor of 532,574, we have to find the factors of both numbers and list the highest common factor.
The factors of 532 are 1, 2, 4, 7, 14, 19, 28, 38, 76, 133, 266, 532
The factors of 574 are 1, 2, 7, 14, 41, 82, 287, 574
The HCF of 532,574 is 14.
Lets's calculate GCF of 532,574
| 2 | 532, 574 |
| 7 | 266, 287 |
| 38, 41 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 532,574 By Matching Biggest Common Factor Method
Now, list down the factors of 532
:1,2,4,7,14,19,28,38,76,133,266,532
Now, list down the factors of 574
:1,2,7,14,41,82,287,574
Greatest Common Factor
We found the factors 532,574 . The biggest common factor number is the GCF number.
So the greatest common factor 532,574 is 14.
Lets's calculate LCM of 68,1509
Given numbers has no common factors except 1. So, there LCM is their product i.e 102612
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/102612
Therefore, the GCF of Fractions 532/68,574/1509 is 14/102612
Least Common Multiple of 68,1509 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 68,1509 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(68,1509) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(68,1509) x common factors =1 x 1 = 1
LCM(68,1509) = ( 68 × 1509 ) / 1
LCM(68,1509) = 102612 / 1
LCM(68,1509) = 102612
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FAQs on GCF of Fractions of 532/68, 574/1509
1. What is the HCF of 532,574?
The HCF of 532,574 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 532/68, 574/1509?
Answer: GCF of Numerators as per given numbers 532/68, 574/1509 is
GCF of Numerators i.e. for 532,574 is 14
LCM of denominators i.e. for 68,1509 is 102612.
Thus, GCF of Fractions is 14/102612.Finally, GCF of Fractions for 532/68, 574/1509 is 14/102612.