GCF of 352/258, 192/714
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 352/258, 192/714 i.e 32/30702 easily. The following is the detailed procedure to determine the greatest common factor of fractions 352/258, 192/714.
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 352/258,192/714?
Given fractions are 352/258,192/714
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 352/258,192/714, numerators are 352,192
Denominators are 258,714
The GCF of 352,192 is 32 .
LCM of 258,714 is 30702.
The greatest common factor of 352/258,192/714 = [GCF of 352,192]/[LCM of 258,714]= 32/30702
Therefore, the GCF of 352/258,192/714 is 32/30702.
To find the highest common factor of 352,192, we have to find the factors of both numbers and list the highest common factor.
The factors of 352 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, 352
The factors of 192 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192
The HCF of 352,192 is 32.
Lets's calculate GCF of 352,192
| 2 | 352, 192 |
| 2 | 176, 96 |
| 2 | 88, 48 |
| 2 | 44, 24 |
| 2 | 22, 12 |
| 11, 6 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 = 32
Greatest Common Factor of 352,192 By Matching Biggest Common Factor Method
Now, list down the factors of 352
:1,2,4,8,11,16,22,32,44,88,176,352
Now, list down the factors of 192
:1,2,3,4,6,8,12,16,24,32,48,64,96,192
Greatest Common Factor
We found the factors 352,192 . The biggest common factor number is the GCF number.
So the greatest common factor 352,192 is 32.
Lets's calculate LCM of 258,714
| 2 | 258, 714 |
| 3 | 129, 357 |
| 43, 119 |
∴ So the LCM of the given numbers is 2 x 3 x 43 x 119 = 30702
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 32/30702
Therefore, the GCF of Fractions 352/258,192/714 is 32/30702
Least Common Multiple of 258,714 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 258,714 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(258,714) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(258,714) x common factors =6 x 1 = 6
LCM(258,714) = ( 258 × 714 ) / 6
LCM(258,714) = 184212 / 6
LCM(258,714) = 30702
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FAQs on GCF of Fractions of 352/258, 192/714
1. What is the HCF of 352,192?
The HCF of 352,192 is 32
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 352/258, 192/714?
Answer: GCF of Numerators as per given numbers 352/258, 192/714 is
GCF of Numerators i.e. for 352,192 is 32
LCM of denominators i.e. for 258,714 is 30702.
Thus, GCF of Fractions is 32/30702.Finally, GCF of Fractions for 352/258, 192/714 is 32/30702.