# Playing With Numbers

#### Tests for Divisibility of Numbers

Divisibility by 2. If a number has any of the digits 0, 2, 4, 6 or 8 in its one’s place, then it is divisible by 2.

Divisibility by 3. If the sum of the digits of a number is a multiple of 3, then it is divisible by 3.

Divisibility by 4. A number with 2 or more digits is divisible by 4 if the number formed by its last two digits is divisible by 4.

Divisibility by 5. If a number has either 0 or 5 in its one’s place, then it is divisible by 5.

Divisibility by 6. If a number is divisible by 2 and 3 both, then it is divisible by 6.

Divisibility by 7. Remove the last digit, double it, subtract it from the truncated original number and continue doing this until only one digit remains. If this is 0 or 7, then the original number is divisible by 7.

Divisibility by 8. A number with 3 or more digits (if it is less, put zero(s) to the left) is divisible by 8, if the number formed by the last three digits is divisible by 8.

Divisibility by 9. If the sum of the digits of a number is divisible by 9, then the number itself is divisible by 9.

Divisibility by 10. If a number has 0 in the ones place, then it is divisible by 10.

Divisibility by 11. Find the difference between the sum of the digits at odd places (from the right) and the sum of the digits at even places (from the right) of the number. If the difference is either 0 or divisible by 11, then the number is divisible by 11.

Exercise 1. Using divisibility tests, determine which of the following numbers are divisible by 2; 4; by 8:

(a) 562 (b) 1800 (c) 2160 (d) 5600 (e) 6000 (f) 12158 (g) 14570 (h) 21094 (i) 726362 (j) 31795082

Exercise 2. Using divisibility tests, determine which of following numbers are divisible by 3:

(a) 111 (b) 1256 (c) 4785 (d) 73421 (e) 901352 (f) 87654367 (g) 127900184

Exercise 3. Using divisibility tests, determine which of following numbers are divisible by 5:

(a) 111432 (b) 1256765 (c) 4785009 (d) 734216743 (e) 9013521235

Exercise 4. Using divisibility tests, determine which of following numbers are divisible by 6:

(a) 297144 (b) 1258 (c) 4335 (d) 61233 (e) 901352 (f) 438750 (g) 1790184 (h) 12583 (i) 639210 (j) 17852

Exercise 5. Using divisibility tests, determine which of following numbers are divisible by 7; 9; by 10:

(a) 3750 (b) 768328 (c) 3453035 (d) 960102133 (e) 901635821 (f) 4387500090

Exercise 6. Using divisibility tests, determine which of the following numbers are divisible by 11:

(a) 5445 (b) 10824 (c) 7138965 (d) 70169308 (e) 10000001 (f) 901153

Exercise 7. Determine if 25110 is divisible by 45.