GCF of 980/462, 315/972
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 980/462, 315/972 i.e 35/74844 easily. The following is the detailed procedure to determine the greatest common factor of fractions 980/462, 315/972.
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 980/462,315/972?
Given fractions are 980/462,315/972
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 980/462,315/972, numerators are 980,315
Denominators are 462,972
The GCF of 980,315 is 35 .
LCM of 462,972 is 74844.
The greatest common factor of 980/462,315/972 = [GCF of 980,315]/[LCM of 462,972]= 35/74844
Therefore, the GCF of 980/462,315/972 is 35/74844.
To find the highest common factor of 980,315, we have to find the factors of both numbers and list the highest common factor.
The factors of 980 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980
The factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315
The HCF of 980,315 is 35.
Lets's calculate GCF of 980,315
| 5 | 980, 315 |
| 7 | 196, 63 |
| 28, 9 |
∴ So the GCF of the given numbers is 5 x 7 = 35
Greatest Common Factor of 980,315 By Matching Biggest Common Factor Method
Now, list down the factors of 980
:1,2,4,5,7,10,14,20,28,35,49,70,98,140,196,245,490,980
Now, list down the factors of 315
:1,3,5,7,9,15,21,35,45,63,105,315
Greatest Common Factor
We found the factors 980,315 . The biggest common factor number is the GCF number.
So the greatest common factor 980,315 is 35.
Lets's calculate LCM of 462,972
| 2 | 462, 972 |
| 3 | 231, 486 |
| 77, 162 |
∴ So the LCM of the given numbers is 2 x 3 x 77 x 162 = 74844
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 35/74844
Therefore, the GCF of Fractions 980/462,315/972 is 35/74844
Least Common Multiple of 462,972 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 462,972 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(462,972) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(462,972) x common factors =6 x 1 = 6
LCM(462,972) = ( 462 × 972 ) / 6
LCM(462,972) = 449064 / 6
LCM(462,972) = 74844
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FAQs on GCF of Fractions of 980/462, 315/972
1. What is the HCF of 980,315?
The HCF of 980,315 is 35
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 980/462, 315/972?
Answer: GCF of Numerators as per given numbers 980/462, 315/972 is
GCF of Numerators i.e. for 980,315 is 35
LCM of denominators i.e. for 462,972 is 74844.
Thus, GCF of Fractions is 35/74844.Finally, GCF of Fractions for 980/462, 315/972 is 35/74844.