Cluster · Number Theory - Remainders and Divisibility

d
Clusters / #1269
tight score 0.09

Remainders Divisibility and Division Problems
Questions
416
Questions in this cluster
414 total
Question Category Subtype Difficulty

When a number is divided by 7, leaves 1 as the remainder. When the cube of this number is divided by 7, what will be the remainder?

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quant intermediate

Which is the largest number that divides each of 1036, 1813 and 3885 without leaving any remainder?

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quant intermediate

A number when divided by 78 gives the quotient 280 and the remainder 0. If the same number is divided by 65. what Will be the value of the remainder?

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quant intermediate

When m is divided by 7, the remainder is 5. When 3m is divided by 7, the remainder is:

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quant intermediate

If a number gives 2 as the remainder when it is divided by 5, find the remainder when the square of the number is divided by 5.

pipeline-817
reasoning intermediate

A number when divided by 112 it leaves 31 as remainder. When the same number is divided by 14 and 16 it leaves remainder as A and B respectively then what is the ratio of A and B?

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reasoning intermediate

What is the remainder when 20193 divided by 11?

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reasoning intermediate

What is the second smallest number which upon dividing by 3, 5, 7 and 11 leaves a remainder of 2 in each case?

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reasoning intermediate

Find the remainder when (1723888 + 1235222)  is divided by 4.

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reasoning intermediate

x is the least possible natural number that is added to 85 to make it divisible by 13. Now if resultant number is squared and then x is added and is divided by 23, the remainder will be?

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reasoning intermediate

Without doing the actual division, find the remainder when 28735429 is divided by 9.

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mp_police intermediate

When a number is divided by 7, it leaves 1 as the remainder. When the cube of this number is divided by 7, what will be the remainder?

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mp_police intermediate

Find the number when successively divided 3, 5, and 7, leaving the remainder 2, 1, and 3, respectively, and the last quotient is 3.

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mp_police intermediate

The divisor is 11 times the quotient and 5 times the remainder. If the remainder is 44, then the dividend is:

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mp_police intermediate

Which is the largest number that divides each of 1036, 1813 and 3885 without leaving any remainder?

pipeline-1306039
mp_police intermediate

On dividing a certain number by 304, we get 43 as the remainder. If the same number is divided by 16, what will be the remainder?

pipeline-1306151
mp_police intermediate

Find the largest number which divides 203, 359, 437 and 593 leaving remainder 8 in each case.

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mp_police intermediate

Let x be the least number which when divided by 12, 18, 20, 27 and 30, the remainder in each case is 2 and x is divisible by 47. If the HCF of x and 1932 is y, then the sum of the digits of y is?

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mp_police intermediate

The difference between two numbers is 3820. The quotient and remainder are respectively 32 and 7 when the larger number is divided by the smaller one. Find the larger number.

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mp_police intermediate

When 1395, 2247, and 3738 are divided by a certain two-digit number k, the remainder in each case is p. What is the value of (2k - 3p)?

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mp_police intermediate

When a positive integer 'n' is divided by 12, the remainder is 5. What will be the remainder if 8n+ 7 is divided by 22?

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mp_police intermediate

Find the remainder when 32 × 33 × 34 × 35 × 36 × 37 is divided by 17.

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mp_police intermediate

Find the smallest 5-digit number which when divided by 15, 20 and 25 leaves remainders 7, 12 and 17, respectively.

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mp_police intermediate

What will be the remainder when 31 × 32 × 33 is divided by 5?

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mp_police intermediate
When a number n is divided by 5. the remainder is 2. When n2 is divided by 5. The remainder will be:
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mp_police intermediate

Two positive numbers differ by 2134. When the greater number is divided by the smaller number, the quotient is 2 and the remainder is 147. What is the HCF of the greater of the two given numbers and 4225?

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mp_police intermediate

What is the remainder when 38 is divided by 7?

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mp_police intermediate

Find the remainder when 920 + 2 is divided by 4.

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mp_police intermediate

What is the remainder when we divide 450 + 750 by 65?

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mp_police intermediate

When a number is divided by 7611 gives the remainder 91. What will be the remainder when the same number is divided by 59?

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mp_police intermediate

When 93, 119, and 158 are divided by the integer n (n > 1), the remainder in each case is d. What is the value of (n + d)?

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mp_police intermediate

In a division problem, the divisor is 12 times the quotient and 9 times the remainder. If the remainder is 96, then find the dividend.

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mp_police intermediate

If N = (243 + 253 + 263 + 273) is divided by 102, then find the remainder.

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bihar_police intermediate

If a natural number when divided by 4, 5, 7, and 6 leaves a remainder of 3 in each case, then what is the smallest possible three-digit natural number?

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bihar_police intermediate

If a natural number, when divided by 5, 6, and 7, leaves a remainder of 4, in each case, then what is the smallest possible three-digit natural number?

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bihar_police intermediate

 A number ‘y’ when divided by 225 leaves 33 as the remainder. The same number when divided by 15 leaves ‘z’ as the remainder. The value of z is:

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bihar_police intermediate

When 2256 is divided by 17, the remainder would be:

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rajasthan intermediate

The divisor is 4 times the quotient and 3 times the remainder. Find the dividend if the remainder is 20.

 

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rajasthan intermediate

The least multiple of 23 when divided by 18, 21, and 24 leaves the remainder 7. 10, and 13 respectively. The number is:

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rajasthan intermediate

When 2525 is divided by 26, the remainder is ?

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up_police intermediate

What is the least number that when divided by 11, 13, 19 leaves the remainder of 7 in each case?

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up_police intermediate

A number when divided by 234 gives the remainder 36. What will be the remainder when it is divided by 13?

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up_police intermediate

Find the remainder when 32 × 33 × 34 × 35 × 36 × 37 is divided by 17.

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up_police intermediate

The remainder of the term 9 + 92 + ... + 9(2n+1) when divided by 6 is:

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up_police intermediate

When 2256 is divided by 17, the remainder would be:

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up_police intermediate

In a division sum, the divisor is 13 times the quotient and 6 times the remainder. If the remainder is 39, then the dividend is:

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up_police intermediate

What is the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder?

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up_police intermediate

When all the students of a school are arranged in rows of 16 students, 5 students are left out. All students were arranged in rows of 20 students 13 are left out. What is the minimum number of students in the school?

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up_police intermediate
Find the least number which when divided by 4, 9, 12, and 15, leaves the remainder 3 in each case.
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up_police intermediate

The smallest number when divided by 8, 13 and 17 leaves a remainder 5. Find the remainder when the same number is divided by 9.

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up_police intermediate
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