Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.
Answer: A
Required number = H.C.F. of \((91 - 43)\), \((183 - 91)\) and \((183 - 43)\)
= H.C.F. of \(48, 92\) and \(140 = 4\).
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The greatest four digit number which is divisible by 15, 25, 40, 75 is
Answer: B
We want 4 digit number, so option A is not the answer
Now we want greatest numnber, So out of remaining options, 9600 is greatest
9600 is divisible by 25, 75, 40, and 15
So answer is 9600
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Find the H.C.F. of 54, 288, 360
Answer: A
Using factorization method,
\(18 = 2 \times 3^2\)
\(288 = 2^5 \times 3^2\)
\(360 = 2^3 \times 3^2 \times 5\)
So H.C.F. will be minimum term present in all three,
i.e. \(2 \times 3^2 = 18\)
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Find the H.C.F. of
\(2^{2}\times 3^{2}\times 7^{2},2\times 3^{4} \times 7\)
Answer: B
HCF is Highest common factor, so we need to get the common highest factors among given values.
So we get,
\(2 \times 3 \times 3 \times 7 = 126\)
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The L.C.M. of two numbers is 14560 and their H.C.F. is 13. If one of them is 416, the other is
Answer: B
416 X number = 14560 X 13
Therefore, numbr is 455
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A number when divided by 893 the remainder is 193. What will be the remainder when it is divided by 47?
Answer: B
Number is divided by 893. Remainder = 193.
Also, we observe that 893 is exactly divisible by 47,
So now simply divide the remainder by 47
Remainder is 5
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The least number which when divided by the numbers 3, 5, 6, 8, 10 and 12 leaves in each case a remainder 2 but which when divided by 13 leaves no remainder?
Answer: C
No answer description available for this question.
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The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:
Answer: C
Greatest number of 4-digits is 9999.
L.C.M. of 15, 25, 40 and 75 is 600.
On dividing 9999 by 600, the remainder is 399.
Required number,
\((9999 - 399) = 9600\)
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3 birds fly along the circumference of a jungle. They complete one round in 27 minutes, 45 minutes and 63 minutes respectively. Since they start together, when will they meet again at the starting position?
Answer: A
We need the instance which means the LCM of times of all 3 birds.
Therefore, LCM = 9 X 3 X 5 X 7 = 945 = 945 minutes
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252 can be expressed as a product of primes as:
Answer: A
Clearly, \(252 = 2 \times 2 \times 3 \times 3 \times 7\)
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