GCF of 86/30, 762/14, 972/564
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 86/30, 762/14, 972/564 i.e 2/19740 easily. The following is the detailed procedure to determine the greatest common factor of fractions 86/30, 762/14, 972/564.
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 86/30,762/14,972/564?
Given fractions are 86/30,762/14,972/564
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 86/30,762/14,972/564, numerators are 86,762,972
Denominators are 30,14,564
The GCF of 86,762,972 is 2 .
LCM of 30,14,564 is 19740.
The greatest common factor of 86/30,762/14,972/564 = [GCF of 86,762,972]/[LCM of 30,14,564]= 2/19740
Therefore, the GCF of 86/30,762/14,972/564 is 2/19740.
To find the highest common factor of 86,762,972, we have to find the factors of both numbers and list the highest common factor.
The factors of 86 are 1, 2, 43, 86
The factors of 762 are 1, 2, 3, 6, 127, 254, 381, 762
The factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972
The HCF of 86,762,972 is 2.
Lets's calculate GCF of 86,762,972
| 2 | 86, 762, 972 |
| 43, 381, 486 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 86,762,972 By Matching Biggest Common Factor Method
Now, list down the factors of 86
:1,2,43,86
Now, list down the factors of 762
:1,2,3,6,127,254,381,762
Now, list down the factors of 972
:1,2,3,4,6,9,12,18,27,36,54,81,108,162,243,324,486,972
Greatest Common Factor
We found the factors 86,762,972 . The biggest common factor number is the GCF number.
So the greatest common factor 86,762,972 is 2.
Lets's calculate LCM of 30,14,564
| 2 | 30, 14, 564 |
| 3 | 15, 7, 282 |
| 5, 7, 94 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 7 x 94 = 19740
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/19740
Therefore, the GCF of Fractions 86/30,762/14,972/564 is 2/19740
Least Common Multiple of 30,14,564 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 30,14,564 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(30,14,564) = 2
common factors(in case of two or more numbers have common factors) = 6
GCF(30,14,564) x common factors =2 x 6 = 12
LCM(30,14,564) = ( 30 × 14 × 564 ) / 12
LCM(30,14,564) = 236880 / 12
LCM(30,14,564) = 19740
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FAQs on GCF of Fractions of 86/30, 762/14, 972/564
1. What is the HCF of 86,762,972?
The HCF of 86,762,972 is 2
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 86/30, 762/14, 972/564?
Answer: GCF of Numerators as per given numbers 86/30, 762/14, 972/564 is
GCF of Numerators i.e. for 86,762,972 is 2
LCM of denominators i.e. for 30,14,564 is 19740.
Thus, GCF of Fractions is 2/19740.Finally, GCF of Fractions for 86/30, 762/14, 972/564 is 2/19740.