Divisibility Tests for 3

Q.

What is the test of divisibility of 18?

Q.

How many factors of $720$ are divisible by $4$ but not by $16$?

Q.

A number is said to be divisible by 4 if the_______ of the number is divisible by 4.

1. sum of all digits

2. sum of last two digits

3. last two digits

4. unit digit

Q.

The sum of a three digit number and the number formed by the reversal of its digits (if for both the numbers middle digit is 0) is always divisible by 101

1. 11

2. 12

Q.

Determine the HCF of following pairs by finding factors:

(f) $18$ and $36$

Q.

If$p:4$ is an even prime number, $q:6$ is a divisor of $12$and $r$: the HCF of $4$and $6$is$2$, then which one of the following is correct?

1. $(p\wedge q)$

2. $(p\vee q)\wedge ~r$

3. $~(q\wedge r)\vee p$

4. $~p\vee (q\wedge r)$

5. $p\leftrightarrow (q\wedge r)$

Q.

Find the greatest number which exactly divides $81,117$

Q. In each of the following numbers. replace * by the smallest number to make it divisible by 11:

(i) 86 * 72
(ii) 467 * 91
(iii) 9 * 8071

Q.

Question 79

In the following question, state whether the given statement is true (T) or false (F).
If a number divides three numbers exactly, it must divide their sum exactly.

Q. Which of the following statements are true?

(i) If a number is divisible by 3, it must be divisible by 9.
(ii) If a number is divisible by 9, it must be divisible by 3.
(iii) If a number is divisible by 4, it must be divisible by 8.
(iv) If a number is divisible by 8, it must be divisible by 4.
(v) A number is divisible by 18, if it is divisible by both 3 and 6.
(vi) If a number is divisible by both 9 and 10, it must be divisible by 90.
(vii) If a number exactly divides the sum of two numbers, it must exactly divide the numbers separately.
(viii) If a number divides three numbers exactly, it must divide their sum exactly.
(ix) If two numbers are co-prime, at least one of them must be a prime number
(x) The sum of two consecutive odd numbers is always divisible by 4.

Q. Find the smallest number of six digits that is exactly divisible by $40,35,85,119$ and $136.$

1. $184720$
2. $164720$
3. $134720$
4. $104720$

Q. In each of the following numbers, replace * by the smallest number to make it divisible by 9:

(i) 67 * 19
(ii) 66784 *
(iii) 538 * 8

Q. What least value should be given to * so that the number 915*26 is divisible by 9?

(a) 1
(b) 4
(c) 2
(d) 6

Q. The smallest 4-digitnumber exactly divisible by $12,15,20and35$ is ...........

1. $1,000$
2. $1,160$
3. $1,260$
4. none of these

Q.

There is a 2 - D plane filled with 3 digit, 2 digit and single digit numbers. A, B and C are 3 digit numbers. The digit at the hundreds place is the head and the digit at units place is tail of the number. There are no mirrors in this plane. So, no number can see its own tail. A, B and C are good friends. Since, A can see B's and C's tail, it tells them that they both are divisible by 4. B and C tell A that it is divisible by 2. One day a 3D Mathematician comes and adds A, B and C to form a 4 digit number. This new number (A + B + C), must be divisible by:

1. 2

2. 2 and 4

3. 8

4. 4

Q. The number 4a6 is divisible by 3. Find the least value of a.

1. 7
2. 4
3. 2
4. 0

Q.

Question 80

In the following question, state whether the given statement is true (T) or false (F).
If a number exactly divides the sum of three numbers, it must exactly divide the numbers separately.

Q. What least value should be given to * so that the number 6342*1 is divisible by 3?

(a) 0
(b) 1
(c) 2
(d) 3

Q. what is the divisible rule of 100

Q.

Question 5 (b)

Write the smallest digit and the largest digit in the blank for the given number so that the number formed is divisibly by 3:
4765__2

Q.

State whether the following statement is True or False

If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately

1. True
2. False

Q. The number $4a6$ is divisible by 3. Find the least value of $a$.

Q. If 3P is a number which is divisible by 2 and 3, find the possible values of P.

1. \N
2. 4
3. 6
4. 8

Q. If 74z5 is a multiple of 3, where z is a digit, then what are the possible values of z?

1. 2
2. 5
3. 8
4. All of these

Q. If the of digits of a number is divisible by 3, then the number is divisible by 3.

1. 2
2. 3
3. 4

Q. In each of the following replace $\ast$ by (i) the smallest digit $0$ the greatest digit so that the number formed is divisible by $6$ :
$5825\ast 34$

Q. Using each of the digit $1,2,3$ and $4$ only once, determine the smallest $4$ digit number divisible by $4$.

Q.

What is 15 divided by 3?

1. 7

2. 9

3. 5

4. 6

Q. Which of the following numbers completely divides 225?

1. 6
2. 2
3. 4
4. 3

Q. Which of the following numbers is completely divisible by 3?

1. 327
2. 428
3. 124
4. 305