GCF of 710/14, 630/54, 945/20
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 710/14, 630/54, 945/20 i.e 5/3780 easily. The following is the detailed procedure to determine the greatest common factor of fractions 710/14, 630/54, 945/20.
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 710/14,630/54,945/20?
Given fractions are 710/14,630/54,945/20
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 710/14,630/54,945/20, numerators are 710,630,945
Denominators are 14,54,20
The GCF of 710,630,945 is 5 .
LCM of 14,54,20 is 3780.
The greatest common factor of 710/14,630/54,945/20 = [GCF of 710,630,945]/[LCM of 14,54,20]= 5/3780
Therefore, the GCF of 710/14,630/54,945/20 is 5/3780.
To find the highest common factor of 710,630,945, we have to find the factors of both numbers and list the highest common factor.
The factors of 710 are 1, 2, 5, 10, 71, 142, 355, 710
The factors of 630 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, 630
The factors of 945 are 1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 105, 135, 189, 315, 945
The HCF of 710,630,945 is 5.
Lets's calculate GCF of 710,630,945
| 5 | 710, 630, 945 |
| 142, 126, 189 |
∴ So the GCF of the given numbers is 5 = 5
Greatest Common Factor of 710,630,945 By Matching Biggest Common Factor Method
Now, list down the factors of 710
:1,2,5,10,71,142,355,710
Now, list down the factors of 630
:1,2,3,5,6,7,9,10,14,15,18,21,30,35,42,45,63,70,90,105,126,210,315,630
Now, list down the factors of 945
:1,3,5,7,9,15,21,27,35,45,63,105,135,189,315,945
Greatest Common Factor
We found the factors 710,630,945 . The biggest common factor number is the GCF number.
So the greatest common factor 710,630,945 is 5.
Lets's calculate LCM of 14,54,20
| 2 | 14, 54, 20 |
| 7, 27, 10 |
∴ So the LCM of the given numbers is 2 x 7 x 27 x 10 = 3780
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/3780
Therefore, the GCF of Fractions 710/14,630/54,945/20 is 5/3780
Least Common Multiple of 14,54,20 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 14,54,20 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(14,54,20) = 2
common factors(in case of two or more numbers have common factors) = 2
GCF(14,54,20) x common factors =2 x 2 = 4
LCM(14,54,20) = ( 14 × 54 × 20 ) / 4
LCM(14,54,20) = 15120 / 4
LCM(14,54,20) = 3780
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FAQs on GCF of Fractions of 710/14, 630/54, 945/20
1. What is the HCF of 710,630,945?
The HCF of 710,630,945 is 5
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 710/14, 630/54, 945/20?
Answer: GCF of Numerators as per given numbers 710/14, 630/54, 945/20 is
GCF of Numerators i.e. for 710,630,945 is 5
LCM of denominators i.e. for 14,54,20 is 3780.
Thus, GCF of Fractions is 5/3780.Finally, GCF of Fractions for 710/14, 630/54, 945/20 is 5/3780.