Cluster · Number System Divisibility and Perfect Squares

d
Clusters / #1206
tight score 0.09

Divisibility Rules and Missing Digits
Questions
604
Questions in this cluster
604 total
Question Category Subtype Difficulty

If the number a525b973 is divisible by 33, then which of the following could be (a × b)?

pipeline-496694
rpf intermediate

How many factors of 1080 are perfect squares? 

pipeline-492579
rpf intermediate

If the number x869y is divisible by 3 and 4 then, what will be the least value of (2x + 5y)?

pipeline-490308
rpf intermediate

A three-digit number N27 is divisible by 9. What will be a possible value of N, if N is a single digit?

pipeline-489666
rpf intermediate

Consider the given numbers: 12990, 55464, 507455, 1874736, and 22074056

which is completely divisible by 6 and 8 both?

pipeline-490317
rpf intermediate

The least number by which 2400 must be divided to get a number that is a perfect square is?

pipeline-481725
rpf intermediate

If 4p75684q2 is divisible by 72 then, find the value of p + q.

pipeline-489668
rpf intermediate

Find the total number of prime factors of 148.

pipeline-484305
rpf intermediate

If 'M' is the smallest perfect square number, which is exactly divisible by 12, 15 and 18, then find the sum of the digits of the quotient obtained, when M is divided by 25.

pipeline-1310625
defence intermediate

A company is printing a limited number of 5-digit numbers. The company wants to know the smallest and largest 5-digit numbers that are divisible by 15, 10, and 8. Find the numbers.

pipeline-1318927
defence intermediate

If a 10-digit number 24y68x996z is divisible by 72 then, find the value of (2z - xy). (where the value of x, y < 5 and x, y, z ≠ 0)

pipeline-1318941
defence intermediate

350 + 926 + 2718 + 928 + 929 is divisible by which of the following integers?

pipeline-1318922
defence intermediate

If the nine-digit number 708x6y8z9 is divisible by 99, then what is the value of x + y + z?

pipeline-1305321
defence intermediate

625 + 626 + 627 + 628 is divisible by:

pipeline-1305322
defence intermediate

If the 6-digit numbers x35624 and 1257y4 are divisible by 11 and 72, respectively, then what is the value of (5x - 2y)?

pipeline-1305320
defence intermediate

The smallest prime number that is a divisor of 17408 is 2 (17408 = 17 × 210). What is the sum of the digits of the greatest prime number that is a divisor of 17391? 

pipeline-1296663
defence intermediate

For what least value of n, 22n + 2n is completely divided by 6, where n is an integer?

pipeline-1296597
defence intermediate

A number is divisible by 11 if and only if the difference of the sum of the digits in the even and odd positions in the number is:

pipeline-1296651
defence intermediate

If the 7-digit number 612x97y is divisible by 72, and the 6-digit number 34z178 is divisible by 11, then the value of (x - 2y + 3z) is:

pipeline-1290097
defence intermediate

Which one of the following is correct regarding the Statements given below?

Statement 1: 210 is the smallest natural number having exactly 11 factors.

Statement 2: 211 is the smallest natural number having exactly 12 factors.

Statement 3: 212 is the smallest natural number having exactly 13 factors.

pipeline-1290116
defence intermediate

If the 9-digit number 5x82y6588 is exactly by 99 (x + y < 10), then what is the value of y - x?

pipeline-1296687
defence intermediate

If the number 756534P57Q is divisible by 72, then find the value of 2P + Q.

pipeline-1290100
defence intermediate

K being any odd number greater than 1, k33 - k is always divisible by

pipeline-1296671
defence intermediate

If the 6-digit number 479xy9 is divisible by each of 7, 11, 13, then (x - y) is equal to -

pipeline-1290129
defence intermediate

If the number 72864*@ is divisible by both 8 and 5, then what digits will come in place of * and @ respectively?

pipeline-1296626
defence intermediate

If the nine-digit number 3422213AB is divisible by 99, then what is the value of 2A + B?

pipeline-1272505
defence intermediate

The number 9730 - 1430 is divisible by?

pipeline-1272501
defence intermediate

How many natural numbers less than 1000 are divisible by 5 or 7 but NOT by 35?

pipeline-1266175
defence intermediate

What is the smallest number that is a multiple of 13, 15, 4, 21 and 2?

pipeline-1251961
defence intermediate

Find the lowest positive value of (c – b) such that the 7-digit number 1738b9c is divisible by 12.

pipeline-1251963
defence intermediate

A number is cube of 53. When 7 times of 57 is subtracted from the number, then the resultant number which is formed will be divisible by:

pipeline-1266171
defence intermediate

How many 100 digit even number?

pipeline-1266174
defence intermediate

A number is cube of 53. When 7 times of 57 is subtracted from the number, then the resultant number which is formed will be divisible by:

pipeline-1266143
defence intermediate

The product of four consecutive numbers is always divisible by which of the following numbers?

pipeline-1251906
defence intermediate

Replace * by the smallest digit so that 723*56* is divisible by 6.

pipeline-1265965
ib intermediate

If the seven - digit number 49x29y6 is divisible by 72, then what will be the value of (x + 2y) for the largest value of x and y?

pipeline-1241983
defence intermediate

The product of four consecutive numbers is always divisible by which of the following numbers?

pipeline-1266076
ib intermediate

How many factors of the number 28 × 36 × 54 ×105 are multiples of 120?

pipeline-1241963
defence intermediate

There exists a natural number N which is 50 times its own logarithm to the base 10, then the sum of the digits in N is

pipeline-1242001
defence intermediate

(2310 - 1024) is not divisible by?

pipeline-1242005
defence intermediate

If a 9-digit number 609a5b9c9 is divided by 99, then (a + b + c) is equal to:

pipeline-1259342
ib intermediate

If 3c2933k is divisible by both 5 and 11, where c and k are single digit natural numbers, then c + k = ______.

pipeline-1259569
ib intermediate

Which of the following numbers is divisible by 36?

pipeline-1264291
ib intermediate

The five-digit number 45yz0 is divisible by 40. What is the maximum possible value of (y + z)?

pipeline-1255973
ib intermediate

If 5A72B is divisible by 11, then what is the value of B - A?

pipeline-1253393
ib intermediate

The number 4,29,714 is divisible by:

pipeline-1255177
ib intermediate

How many numbers up to 980 are divisible by both 3 and 7?

pipeline-1256062
ib intermediate

Find the smallest four-digit number which is divisible by 4, 8, 12, and 16.

pipeline-1253000
ib intermediate

What is the least positive value of A in the number 34278A2597, which is divisible by 9? 

pipeline-1251826
ib intermediate

If the 8- digit number 7x5739y2 is divisible by 88, then the largest possible value of (4x + 3y) is :

pipeline-1241560
ib intermediate
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