GCF of 1972/216, 8288/8292
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1972/216, 8288/8292 i.e 4/149256 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1972/216, 8288/8292.
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 1972/216,8288/8292?
Given fractions are 1972/216,8288/8292
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 1972/216,8288/8292, numerators are 1972,8288
Denominators are 216,8292
The GCF of 1972,8288 is 4 .
LCM of 216,8292 is 149256.
The greatest common factor of 1972/216,8288/8292 = [GCF of 1972,8288]/[LCM of 216,8292]= 4/149256
Therefore, the GCF of 1972/216,8288/8292 is 4/149256.
To find the highest common factor of 1972,8288, we have to find the factors of both numbers and list the highest common factor.
The factors of 1972 are 1, 2, 4, 17, 29, 34, 58, 68, 116, 493, 986, 1972
The factors of 8288 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 37, 56, 74, 112, 148, 224, 259, 296, 518, 592, 1036, 1184, 2072, 4144, 8288
The HCF of 1972,8288 is 4.
Lets's calculate GCF of 1972,8288
| 2 | 1972, 8288 |
| 2 | 986, 4144 |
| 493, 2072 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 1972,8288 By Matching Biggest Common Factor Method
Now, list down the factors of 1972
:1,2,4,17,29,34,58,68,116,493,986,1972
Now, list down the factors of 8288
:1,2,4,7,8,14,16,28,32,37,56,74,112,148,224,259,296,518,592,1036,1184,2072,4144,8288
Greatest Common Factor
We found the factors 1972,8288 . The biggest common factor number is the GCF number.
So the greatest common factor 1972,8288 is 4.
Lets's calculate LCM of 216,8292
| 2 | 216, 8292 |
| 2 | 108, 4146 |
| 3 | 54, 2073 |
| 18, 691 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 18 x 691 = 149256
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/149256
Therefore, the GCF of Fractions 1972/216,8288/8292 is 4/149256
Least Common Multiple of 216,8292 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 216,8292 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(216,8292) = 12
common factors(in case of two or more numbers have common factors) = 1
GCF(216,8292) x common factors =12 x 1 = 12
LCM(216,8292) = ( 216 × 8292 ) / 12
LCM(216,8292) = 1791072 / 12
LCM(216,8292) = 149256
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FAQs on GCF of Fractions of 1972/216, 8288/8292
1. What is the HCF of 1972,8288?
The HCF of 1972,8288 is 4
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 1972/216, 8288/8292?
Answer: GCF of Numerators as per given numbers 1972/216, 8288/8292 is
GCF of Numerators i.e. for 1972,8288 is 4
LCM of denominators i.e. for 216,8292 is 149256.
Thus, GCF of Fractions is 4/149256.Finally, GCF of Fractions for 1972/216, 8288/8292 is 4/149256.