GCF of 378/870, 105/492
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 378/870, 105/492 i.e 21/71340 easily. The following is the detailed procedure to determine the greatest common factor of fractions 378/870, 105/492.
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 378/870,105/492?
Given fractions are 378/870,105/492
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 378/870,105/492, numerators are 378,105
Denominators are 870,492
The GCF of 378,105 is 21 .
LCM of 870,492 is 71340.
The greatest common factor of 378/870,105/492 = [GCF of 378,105]/[LCM of 870,492]= 21/71340
Therefore, the GCF of 378/870,105/492 is 21/71340.
To find the highest common factor of 378,105, we have to find the factors of both numbers and list the highest common factor.
The factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105
The HCF of 378,105 is 21.
Lets's calculate GCF of 378,105
| 3 | 378, 105 |
| 7 | 126, 35 |
| 18, 5 |
∴ So the GCF of the given numbers is 3 x 7 = 21
Greatest Common Factor of 378,105 By Matching Biggest Common Factor Method
Now, list down the factors of 378
:1,2,3,6,7,9,14,18,21,27,42,54,63,126,189,378
Now, list down the factors of 105
:1,3,5,7,15,21,35,105
Greatest Common Factor
We found the factors 378,105 . The biggest common factor number is the GCF number.
So the greatest common factor 378,105 is 21.
Lets's calculate LCM of 870,492
| 2 | 870, 492 |
| 3 | 435, 246 |
| 145, 82 |
∴ So the LCM of the given numbers is 2 x 3 x 145 x 82 = 71340
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 21/71340
Therefore, the GCF of Fractions 378/870,105/492 is 21/71340
Least Common Multiple of 870,492 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 870,492 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(870,492) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(870,492) x common factors =6 x 1 = 6
LCM(870,492) = ( 870 × 492 ) / 6
LCM(870,492) = 428040 / 6
LCM(870,492) = 71340
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FAQs on GCF of Fractions of 378/870, 105/492
1. What is the HCF of 378,105?
The HCF of 378,105 is 21
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 378/870, 105/492?
Answer: GCF of Numerators as per given numbers 378/870, 105/492 is
GCF of Numerators i.e. for 378,105 is 21
LCM of denominators i.e. for 870,492 is 71340.
Thus, GCF of Fractions is 21/71340.Finally, GCF of Fractions for 378/870, 105/492 is 21/71340.