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Number Theory: Divisibility and Factors

Practice questions on divisibility rules, prime numbers, LCM, HCF, co-prime numbers, and prime factorization

20 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

Which of the following numbers is divisible by 6?

  1. 67821
  2. 78134
  3. 1258
  4. 297144
Question 2 Multiple Choice (Single Answer)

The LCM of two co-prime numbers is their

  1. Sum
  2. Difference
  3. Product
  4. Quotient
Question 3 Multiple Choice (Single Answer)

Which of the following is a prime number?

  1. 143
  2. 131
  3. 147
  4. 161
Question 4 Multiple Choice (Single Answer)

In a morning walk, three boys step off together. Their steps measure 80cm, 85cm and 90cm respectively. What minimum distance should each walk so that all can cover the distance in complete steps?

  1. 61200cm
  2. 12240cm
  3. 7200cm
  4. None of these
Question 5 Multiple Choice (Single Answer)

Three bells toll together at intervals of 9,12,15 minutes. If they start tolling together, after what time will they next toll together?

  1. 1 hour
  2. 1 and half hour
  3. 2 and half hours
  4. 3 hours
Question 6 Multiple Choice (Single Answer)

Which of the following numbers is divisible by 11?

  1. 3333333
  2. 1111111
  3. 22222222
  4. None of these
Question 7 Multiple Choice (Single Answer)

Which of the following are co-prime?

  1. 39, 91
  2. 161, 192
  3. 385, 462
  4. None of these
Question 8 Multiple Choice (Single Answer)

The product of two numbers is 2160 and their HCF is 12. Find the LCM.

  1. 160
  2. 180
  3. 2148
  4. 2172
Question 9 Multiple Choice (Single Answer)

Which of the following is divisible by 3 but not by 9?

  1. 990
  2. 3060
  3. 228
  4. 639210
Question 10 Multiple Choice (Single Answer)

Which of the following numbers are divisible by 8?

  1. 96354142
  2. 37450176
  3. 57064214
  4. 98671402
Question 11 Multiple Choice (Single Answer)

Find the least 5-digit number which is exactly divisible by 20,25, 30?

  1. 10000
  2. 10500
  3. 10200
  4. None of these
Question 12 Multiple Choice (Single Answer)

Find the number which is divisible by 2 but not by 4

  1. 2856
  2. 3060
  3. 1586
  4. 9092
Question 13 Multiple Choice (Single Answer)

Express 84 as sum of 2 odd primes.

  1. 17+67
  2. 81+3
  3. 51+33
  4. 19+65
Question 14 Multiple Choice (Single Answer)

If a number is prime, it must be odd?

  1. True
  2. False
  3. Cannot say
  4. None of these
Question 15 Multiple Choice (Single Answer)

289/391 when reduced to lowest terms is

  1. 11/23
  2. 13/31
  3. 17/31
  4. 17/23
Question 16 Multiple Choice (Single Answer)

Which of the following is the smallest prime number?

  1. 1
  2. 2
  3. 0
  4. 3
Question 17 Multiple Choice (Single Answer)

Find the HCF of 24 and 32

  1. 96
  2. 56
  3. 8
  4. none of these
Question 18 Multiple Choice (Single Answer)

Replace * by the smallest number in 27*4 to make it divisible by 3

  1. 1
  2. 3
  3. 9
  4. 2
Question 19 Multiple Choice (Single Answer)

Give the prime factorization of 1260

  1. 2 x 32 x 52 x 7
  2. 22 x 32 x 5 x 7
  3. 23 x 3 x 5 x 7
  4. 22 x 3 x 52 x 7
Question 20 Multiple Choice (Single Answer)

Find the HCF and LCM of 25, 65

  1. 5, 325
  2. 1,90
  3. 325, 5
  4. 90,1

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