# Worksheet on Divisibility Rules

Worksheet on divisibility rules will help us to practice different types of questions on test of divisibility by 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11. We need to use the divisibility rules to find whether the given number is divisible by 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11.

A quick way to find factors of larger numbers is to perform divisibility test. There are certain rules to check divisibility of numbers.

Divisibility by 2:

A number is divisible by 2, if the digit at ones place is an even number, that is the number ends in 0, 2, 4 or 8. For example, 100, 222, 344, 1658 are divisible by 2.

Divisibility by 3:

A number is divisible by 3, if sum of all its digits is divisible by 3. Let us check if 27648 is divisible by 3. Sum of digits = 2 + 7 + 6 + 4 + 8 = 27; 27 ÷ 3 = 9. Hence 27648 is exactly divisible by 3.

Divisibility by 4:

A number is divisible by 4, if the number formed by its last 2 digits is divisible by 4. Let us check if 1124 is divisible by 4. Number formed by last 2 digits 24 is divisible by 4.

Divisibility by 5:

A number is divisible by 5, if it ends in 0 or 5. For example 100, 225, 605, 8000, 9925 are divisible by 5.

Divisibility by 9:

A number is divisible by 9, if sum of its digits is divisible by 9. Let us check if 16911 is divisible by 9.

Sum of digits = 1 + 6 + 9 + 1 + 1 = 18. It is exactly divisible by 9.

Divisibility by 10:

All numbers ending in 0 are divisible by 10. For example 8000, 9010, 11020, 98670 are divisible by 10.

1. Which of the following numbers are divisible by 2, 5 and 10?

(i) 149

(ii) 19400

(iii) 720345

(iv) 125370

(v) 3000000

2. Check whether the numbers are divisibility by 4:

(i) 23408

(ii) 100246

(iii) 34972

(iv) 150126

(v) 58724

(vi) 19000

(vii) 43938

(viii) 846336

3. In each of the following numbers without doing actual division, determine whether the first number is divisible by the second number:

(i) 3409122; 6

(ii) 17218; 6

(iii) 11309634; 8

(iv) 515712; 8

(v) 3501804; 4

4. 6 is a factor of 12066 and 49320. Is 6 a factor of 49320 + 12066 and 49320 - 12066?

5. Is 9 a factor of the following?

(i) 394683

(ii) 1872546

(iii) 5172354

6. Fill in the smallest digit to make the number divisible by:

(i) by 5 : 7164__, 32197__

(ii) by 3 : 1__43, 47__05, __316

(iii) by 6 : __428, 9__52, 721__

(iv) by 4 : 2462__, 91__ __, 670__

(v) by 8 : 1232__, 59__16, 4642__

7. Using the divisibility rules check whether the number is divisible by the given numbers. Put P (tick) or û (cross).

8. Check using divisibility rules and fill in the boxes using “Yes” or “No”.

9. Which of the two nearest numbers to 19506 are divisible by 9?

(i) The number with unit digit 0 or 5 is divisible by:

(a) 2

(b) 3

(c) 4

(d) 5

(ii) The number with unit digit 0, 2, 4, 6 or 8 is divisible by:

(a) 2

(b) 3

(c) 4

(d) 5

(iii) The number with unit digit 0 is divisible by:

(a) 5

(b) 10

(c) 15

(d) 2

(iv) 3681 is divisible by:

(a) 4

(b) 5

(c) 9

(d) 10

(v) 1170 is not divisible by:

(a) 10

(b) 9

(c) 5

(d) 4

(vi) Which of the following numbers is not divisible by 2?

(a) 1086

(b) 2869

(c) 3364

(d) 7000

(vii) Which of the following numbers is not divisible by 3?

(a) 1173

(b) 2391

(c) 3902

(d) 6048

(viii)  Which of the following numbers is not divisible by 4?

(a) 1084

(b) 3516

(c) 3328

(d) 7001

(ix) Which of the following numbers is not divisible by 10?

(a) 2015

(b) 3000

(c) 4170

(d) 8990

(x) Which of the following numbers is divisible by 9?

(a) 1284

(b) 3510

(c) 4328

(d) 7301

Answers for the worksheet on divisibility rules are given below.

1. (ii) 19400

(iv) 125370

(v) 3000000

2. (i) 23408

(iii) 34972

(v) 58724

(vi) 19000

(viii) 846336

3. (i) Yes

(ii) No

(iii) No

(iv) Yes

(v) Yes

4. Yes

5. (iii) 5172354

6. (i) 0, 0

(ii) 1, 2, 2

(iii) 1, 2, 2

(iv) 0, 00, 0

(v) 0, 0, 4

7. (i) PûûPûP

(ii) ûPûûPû

(iii) PPûPûP

(iv) PûPû, û, û

(v) û, ûûPû û

(vi) PPû, û, ûû

8. (i) Yes, No, Yes, No, No, Yes, No, No

(ii) Yes, Yes, Yes, No, Yes, No, No, Yes

(iii) Yes, No, Yes, No, No, Yes, Yes, No

(iv) Yes, Yes, Yes, No, Yes, No, Yes, Yes

(v) No, Yes, No, No, No, No, No, No

(vi) Yes, Yes, Yes, No, Yes, Yes, No, Yes

(vii) Yes, No, Yes, Yes, No, No, Yes, No

(viii) Yes, No, Yes, Yes, No, No, Yes, No

(ix) No, Yes, No, Yes, No, No, No, No

9. 19503, 19512

10. (i) (d) 5

(ii) (a) 2

(iii) (b) 10

(iv) (c) 9

(d) 10

(v) (d) 4

(vi) (b) 2869

(vii) (c) 3902

(viii)  (d) 7001

(ix) (a) 2015

(x) (b) 3510

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Properties of Divisibility.

Divisible by 2.

Divisible by 3.

Divisible by 4.

Divisible by 5.

Divisible by 6.

Divisible by 7.

Divisible by 8.

Divisible by 9.

Divisible by 10.

Divisible by 11.

Problems on Divisibility Rules

Worksheet on Divisibility Rules