GCF of 42/304, 32/513, 520/774
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 42/304, 32/513, 520/774 i.e 2/352944 easily. The following is the detailed procedure to determine the greatest common factor of fractions 42/304, 32/513, 520/774.
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 42/304,32/513,520/774?
Given fractions are 42/304,32/513,520/774
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 42/304,32/513,520/774, numerators are 42,32,520
Denominators are 304,513,774
The GCF of 42,32,520 is 2 .
LCM of 304,513,774 is 352944.
The greatest common factor of 42/304,32/513,520/774 = [GCF of 42,32,520]/[LCM of 304,513,774]= 2/352944
Therefore, the GCF of 42/304,32/513,520/774 is 2/352944.
To find the highest common factor of 42,32,520, we have to find the factors of both numbers and list the highest common factor.
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 32 are 1, 2, 4, 8, 16, 32
The factors of 520 are 1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 260, 520
The HCF of 42,32,520 is 2.
Lets's calculate GCF of 42,32,520
| 2 | 42, 32, 520 |
| 21, 16, 260 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 42,32,520 By Matching Biggest Common Factor Method
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Now, list down the factors of 32
:1,2,4,8,16,32
Now, list down the factors of 520
:1,2,4,5,8,10,13,20,26,40,52,65,104,130,260,520
Greatest Common Factor
We found the factors 42,32,520 . The biggest common factor number is the GCF number.
So the greatest common factor 42,32,520 is 2.
Lets's calculate LCM of 304,513,774
| 2 | 304, 513, 774 |
| 3 | 152, 513, 387 |
| 3 | 152, 171, 129 |
| 19 | 152, 57, 43 |
| 8, 3, 43 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 19 x 8 x 3 x 43 = 352944
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/352944
Therefore, the GCF of Fractions 42/304,32/513,520/774 is 2/352944
Least Common Multiple of 304,513,774 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 304,513,774 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(304,513,774) = 1
common factors(in case of two or more numbers have common factors) = 342
GCF(304,513,774) x common factors =1 x 342 = 342
LCM(304,513,774) = ( 304 × 513 × 774 ) / 342
LCM(304,513,774) = 120706848 / 342
LCM(304,513,774) = 352944
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FAQs on GCF of Fractions of 42/304, 32/513, 520/774
1. What is the HCF of 42,32,520?
The HCF of 42,32,520 is 2
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 42/304, 32/513, 520/774?
Answer: GCF of Numerators as per given numbers 42/304, 32/513, 520/774 is
GCF of Numerators i.e. for 42,32,520 is 2
LCM of denominators i.e. for 304,513,774 is 352944.
Thus, GCF of Fractions is 2/352944.Finally, GCF of Fractions for 42/304, 32/513, 520/774 is 2/352944.