HCF is the highest common factor which divides all the given numbers exactly.
280 | ) | 364 |
( | 1 | |||||||
280 |
|||||||||||
84 |
) | 280 | ( | 3 | |||||||
252 | |||||||||||
28 | ) | 84 | ( | 3 | |||||||
84 | |||||||||||
0 |
As last divisor is 28, then HCF is 28.
HCF of 144, 192 and 288 is
192 | ) | 288 |
( | 1 | |||||||
192 |
|||||||||||
96 |
) | 192 | ( | 2 | |||||||
192 | |||||||||||
0 |
0 => HCF of 192 and 288 is 96, again HCF of 144 and 192 is
144 | ) | 192 |
( | 1 | |||||||
144 | |||||||||||
48 |
) | 144 | ( | 3 | |||||||
144 | |||||||||||
0 |
HCF of 144, 192 and 288 is 46, 46 liter is the biggest measure, that can be used.
Let the numbers be 2a: 3a: 5a, then HCF of the numbers would be ‘a’
Therefore the numbers are 2 x 15 = 30, 3 x 15 = 45, 5 x 15 = 75
Greatest number that can divide x, y and z, leaving the same remainder in each case is
HCF of ( x – y ), ( y – z ) ( z – x ) [ i.e. the difference between the given numbers]
( 303 – 206) = 97, ( 303 – 109 ) = 194, (206 – 109 ) = 97.
HCF of 97 is 97 and 194 is 97 = > Hence answer is 97
HCF of 24 and 18 is 6 or 6 feet
Therefore answer is 6 feet.
Let the number be 36a + 36b
$$ Then \ a \ + \ b \ = \ \frac{252}{36} \ = \ 7 $$Co – Primes which sums up 7 are => (1,6) (2,5) (3,4)
The numbers can be (36, 216) or (72, 180) or (108, 144)
Out of these we have 108, 144 in the choices.
LCM of 12, 18 and 26 is
$$ \begin{array}{c|lcr} 2 & \text{12} & \text{18} & \text{26} \\ \hline 2 & \text{6} & \text{9} & \text{13} \\ \hline 3 & \text{3} & \text{9} & \text{13} \\ \hline & \text{1} & \text{3} & \text{13} \\ \end{array} $$= > 2^{2} x 3^{2} x 13 or 4 x 9 x 13 = 468
LCM of 24, 32 and 48 is 96.
Required number = 96 + 7 = 113.
LCM of 12, 14, 15 and 18 is 1260.
Largest 4 digit number divisible by 1260 is 8820 { Multiple of 1260 }
( 16 – 8 ) = 8, ( 18 – 10 ) = 8, ( 22 – 14 ) = 8, (27 – 19 ) = 8
LCM of 16, 18, 22 and 27 is 4752
Required number is 4752 – 8 = 4744
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Highest Common Factor / Greatest Common Measure [H.C.F/G.C.M]: The H.C.F. of two or more than two numbers is the greatest number that divides each one of them exactly.
Express each one of the given numbers as the product of prime factors. The product of least powers of common prime factors gives HCF.
The least number which is exactly divisible by each one of the given numbers is called their LCM.
Express each one of the given numbers as the product of prime factors. The product of highest powers of all prime factors gives LCM.
HCF = $\displaystyle \frac{\text{HCF of Numerators}}{\text {LCM of Denominators}}$
LCM = $\displaystyle \frac{\text{LCM of Numerators}}{\text{HCF of Denominators}}$
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