What is HCF of 36/75, 48/150 , 72/135?
Answer: A
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Find the H.C.F. of 2.1, 1.05 and 0.63.
Answer: C
To solve this question quickly, first remove decimal by multiplying each term with 100,
Then terms become 210, 105, 63
Then H.C.F. of above terms = 21
So Answer is 0.21
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If the sum of two numbers is 55 and the H.C.F. and L.C.M. of these numbers are 5 and 120 respectively, then the sum of the reciprocals of the numbers is equal to:
Answer: C
Let the numbers be \(a\) and \(b\).
Then,
\(a + b = 55\) and
\(ab = 5 \times 120 = 600\)
The required sum
\(=\dfrac{1}{a} + \dfrac{1}{b}\\~\\= \dfrac{a+b}{ab}\\~\\=\dfrac{55}{600}\\~\\= \dfrac{11}{120}\)
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Find the greatest number that will divide 400, 435 and 541 leaving 9, 10 and 14 as remainders respectively
Answer: B
H.C.F. of \((400-9, 435-10, 541-14)\)
H.C.F. of \((391, 425, 527) = 17\)
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The Greatest Common Divisor for two numbers is 8 while their Least Common Multiple is 144. Find the other number if one number is 16.
Answer: C
If A and B are two numbers,
A X B = HCF of A and B X LCM of Amand B
Therefore, 16 X ? = 8 X 144
Therefore, ? = 72
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The least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 8 is:
Answer: D
Required number
\(= (L.C.M. of 12, 15, 20, 54) + 8\)
\(= 540 + 8\)
\(= 548\)
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Find the largest number which divides 62,132,237 to leave the same reminder.
Answer: C
H.C.F. of \((237-132), (132-62), (237-62)\)
= H.C.F. of \((70,105,175)\)
\(= 35\)
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Find the H.C.F. of \(\dfrac{2}{3}, \dfrac{4}{6}, \dfrac{8}{27}\)
Answer: A
Formula,
\(H.C.F. = \dfrac{H.C.F. of Numerators}{L.C.M. of Denominators}\)
So,
\(\dfrac{H.C.F. of (2,4,8) }{L.C.M. of (3,6,27)} \\~\\=\dfrac{2}{27}\)
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The least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is:
Answer: D
L.C.M. of 6, 9, 15 and 18 is 90.
Let required number be \(90k + 4\), which is multiple of \(7\).
Least value of k for which \((90k + 4)\) is divisible by \(7\) is \(k = 4.\)
Required number,
\(= (90 \times 4) + 4\)
\(= 364\)
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The sum and HCF of two numbers are 156 and 13. The numbers of such number pairs is
Answer: A
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