GCF of 252/304, 172/168
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 252/304, 172/168 i.e 4/6384 easily. The following is the detailed procedure to determine the greatest common factor of fractions 252/304, 172/168.
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 252/304,172/168?
Given fractions are 252/304,172/168
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 252/304,172/168, numerators are 252,172
Denominators are 304,168
The GCF of 252,172 is 4 .
LCM of 304,168 is 6384.
The greatest common factor of 252/304,172/168 = [GCF of 252,172]/[LCM of 304,168]= 4/6384
Therefore, the GCF of 252/304,172/168 is 4/6384.
To find the highest common factor of 252,172, we have to find the factors of both numbers and list the highest common factor.
The factors of 252 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252
The factors of 172 are 1, 2, 4, 43, 86, 172
The HCF of 252,172 is 4.
Lets's calculate GCF of 252,172
| 2 | 252, 172 |
| 2 | 126, 86 |
| 63, 43 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 252,172 By Matching Biggest Common Factor Method
Now, list down the factors of 252
:1,2,3,4,6,7,9,12,14,18,21,28,36,42,63,84,126,252
Now, list down the factors of 172
:1,2,4,43,86,172
Greatest Common Factor
We found the factors 252,172 . The biggest common factor number is the GCF number.
So the greatest common factor 252,172 is 4.
Lets's calculate LCM of 304,168
| 2 | 304, 168 |
| 2 | 152, 84 |
| 2 | 76, 42 |
| 38, 21 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 38 x 21 = 6384
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/6384
Therefore, the GCF of Fractions 252/304,172/168 is 4/6384
Least Common Multiple of 304,168 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 304,168 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(304,168) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(304,168) x common factors =8 x 1 = 8
LCM(304,168) = ( 304 × 168 ) / 8
LCM(304,168) = 51072 / 8
LCM(304,168) = 6384
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FAQs on GCF of Fractions of 252/304, 172/168
1. What is the HCF of 252,172?
The HCF of 252,172 is 4
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 252/304, 172/168?
Answer: GCF of Numerators as per given numbers 252/304, 172/168 is
GCF of Numerators i.e. for 252,172 is 4
LCM of denominators i.e. for 304,168 is 6384.
Thus, GCF of Fractions is 4/6384.Finally, GCF of Fractions for 252/304, 172/168 is 4/6384.