GCF of 40/27, 756/60, 107/304
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 40/27, 756/60, 107/304 i.e 1/41040 easily. The following is the detailed procedure to determine the greatest common factor of fractions 40/27, 756/60, 107/304.
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 40/27,756/60,107/304?
Given fractions are 40/27,756/60,107/304
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 40/27,756/60,107/304, numerators are 40,756,107
Denominators are 27,60,304
The GCF of 40,756,107 is 1 .
LCM of 27,60,304 is 41040.
The greatest common factor of 40/27,756/60,107/304 = [GCF of 40,756,107]/[LCM of 27,60,304]= 1/41040
Therefore, the GCF of 40/27,756/60,107/304 is 1/41040.
To find the highest common factor of 40,756,107, we have to find the factors of both numbers and list the highest common factor.
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40
The factors of 756 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 54, 63, 84, 108, 126, 189, 252, 378, 756
The factors of 107 are 1, 107
The HCF of 40,756,107 is 1.
Lets's calculate GCF of 40,756,107
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 40,756,107 By Matching Biggest Common Factor Method
Now, list down the factors of 40
:1,2,4,5,8,10,20,40
Now, list down the factors of 756
:1,2,3,4,6,7,9,12,14,18,21,27,28,36,42,54,63,84,108,126,189,252,378,756
Now, list down the factors of 107
:1,107
Greatest Common Factor
We found the factors 40,756,107 . The biggest common factor number is the GCF number.
So the greatest common factor 40,756,107 is 1.
Lets's calculate LCM of 27,60,304
| 2 | 27, 60, 304 |
| 2 | 27, 30, 152 |
| 3 | 27, 15, 76 |
| 9, 5, 76 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 9 x 5 x 76 = 41040
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/41040
Therefore, the GCF of Fractions 40/27,756/60,107/304 is 1/41040
Least Common Multiple of 27,60,304 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 27,60,304 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(27,60,304) = 1
common factors(in case of two or more numbers have common factors) = 12
GCF(27,60,304) x common factors =1 x 12 = 12
LCM(27,60,304) = ( 27 × 60 × 304 ) / 12
LCM(27,60,304) = 492480 / 12
LCM(27,60,304) = 41040
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FAQs on GCF of Fractions of 40/27, 756/60, 107/304
1. What is the HCF of 40,756,107?
The HCF of 40,756,107 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 40/27, 756/60, 107/304?
Answer: GCF of Numerators as per given numbers 40/27, 756/60, 107/304 is
GCF of Numerators i.e. for 40,756,107 is 1
LCM of denominators i.e. for 27,60,304 is 41040.
Thus, GCF of Fractions is 1/41040.Finally, GCF of Fractions for 40/27, 756/60, 107/304 is 1/41040.