GCF of 852/42, 765/49, 598/16
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 852/42, 765/49, 598/16 i.e 1/2352 easily. The following is the detailed procedure to determine the greatest common factor of fractions 852/42, 765/49, 598/16.
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 852/42,765/49,598/16?
Given fractions are 852/42,765/49,598/16
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 852/42,765/49,598/16, numerators are 852,765,598
Denominators are 42,49,16
The GCF of 852,765,598 is 1 .
LCM of 42,49,16 is 2352.
The greatest common factor of 852/42,765/49,598/16 = [GCF of 852,765,598]/[LCM of 42,49,16]= 1/2352
Therefore, the GCF of 852/42,765/49,598/16 is 1/2352.
To find the highest common factor of 852,765,598, we have to find the factors of both numbers and list the highest common factor.
The factors of 852 are 1, 2, 3, 4, 6, 12, 71, 142, 213, 284, 426, 852
The factors of 765 are 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 765
The factors of 598 are 1, 2, 13, 23, 26, 46, 299, 598
The HCF of 852,765,598 is 1.
Lets's calculate GCF of 852,765,598
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 852,765,598 By Matching Biggest Common Factor Method
Now, list down the factors of 852
:1,2,3,4,6,12,71,142,213,284,426,852
Now, list down the factors of 765
:1,3,5,9,15,17,45,51,85,153,255,765
Now, list down the factors of 598
:1,2,13,23,26,46,299,598
Greatest Common Factor
We found the factors 852,765,598 . The biggest common factor number is the GCF number.
So the greatest common factor 852,765,598 is 1.
Lets's calculate LCM of 42,49,16
| 2 | 42, 49, 16 |
| 7 | 21, 49, 8 |
| 3, 7, 8 |
∴ So the LCM of the given numbers is 2 x 7 x 3 x 7 x 8 = 2352
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2352
Therefore, the GCF of Fractions 852/42,765/49,598/16 is 1/2352
Least Common Multiple of 42,49,16 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 42,49,16 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,49,16) = 1
common factors(in case of two or more numbers have common factors) = 14
GCF(42,49,16) x common factors =1 x 14 = 14
LCM(42,49,16) = ( 42 × 49 × 16 ) / 14
LCM(42,49,16) = 32928 / 14
LCM(42,49,16) = 2352
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FAQs on GCF of Fractions of 852/42, 765/49, 598/16
1. What is the HCF of 852,765,598?
The HCF of 852,765,598 is 1
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 852/42, 765/49, 598/16?
Answer: GCF of Numerators as per given numbers 852/42, 765/49, 598/16 is
GCF of Numerators i.e. for 852,765,598 is 1
LCM of denominators i.e. for 42,49,16 is 2352.
Thus, GCF of Fractions is 1/2352.Finally, GCF of Fractions for 852/42, 765/49, 598/16 is 1/2352.