# Divisibility test for 6, 7, 8, 9 and 10

Square, triangular and even numbers

Triangular numbers
These are numbers got after adding consecutive counting numbers e.g.
4
1 = 1,
1 +2 = 3,
1 + 2 + 3 = 6
1+2 + 3 + 4 = 10
1+2 + 3 + 4 +5 = 15
1+2 + 3 + 4+ 5 + 6 = 21
1+2 + 3 + 4 + 5 + 6 + 7= 28
1+2 + 3 + 4 + 5 + 6 + 7 + 8=36
1+2 + 3 + 4 + 5 + 6 + 7 + 8+ 9 = 45
1+2 + 3 + 4 + 5 + 6 + 7 + 8+ 9 + 10 = 55
The triangular numbers are {1,3, 6,10,15, 21,28,36,45,55 …}

Square numbers
A square number is a number got after multiplying a counting number by itself. e.g.
1 x 1 =1
2 x2 =4
3×3 = 9
4 x 4 = 16
5 x 5 = 25
6 x 6 = 36
NB; try it with other counting numbers up to 20

Even numbers
These are numbers which are exactly divisible by 2. e.g. 0, 2, 4, 6, 8, 10, …
All numbers that end with 0,2,4,6 and 8 all even numbers.

Odd numbers
These are numbers which are not exactly divisible by 2 e.g.1, 3, 5, 7, 9,11,13,15, …

Whole numbers
Whole numbers are all counting numbers with zero e.g. 0,1,2,3,4,5,6, …

Counting / Natural numbers

These are all positive numbers on a number line e.g. 1, 2, 3, 4, 5,6, 7, …

Activity

1. List all the triangular numbers less than 30 (show your working)
2. List the triangular numbers less than 40 which are divisible by 3.
3. What is the sum of all numbers from 1 to 10?
4. Find the value of the unknown
a) 1 x 1 = a
b) 2 x 2 = k
c) 4 x k=16
d) 13 x b = 169
5. List elements in a set of counting numbers from 15 to 24
6. Write the counting numbers between 10 and 30 which are divisible by 3.
7. List elements in a set of even numbers below 20.
8. What is the first even number?
9. List members in a set of odd numbers divisible by 3 less than 30
10. List the prime numbers between 10 and 30
11. What is the difference between the prime numbers between 30 and 40?