3
Divisibility tests for 10, 5 and 2
Textbook, pp. 10–12
GoalKnow and use the divisibility tests for 10, 5 and 2.
New words
divisibility test · bo‘linish belgisieven number · juft sonodd number · toq sonlast digit · oxirgi raqam
Explanation
We can tell whether a number is divisible without dividing, just by looking at its digits. A number is divisible by 10 if its last digit is 0. It is divisible by 5 if its last digit is 0 or 5. It is divisible by 2 if its last digit is even: 0, 2, 4, 6 or 8. A number ending in 1, 3, 5, 7 or 9 is odd and is not divisible by 2. These tests depend only on the last digit because 10, 100, 1000 ... are all divisible by 2, 5 and 10.
Worked examples
3,450 is divisible by 10, by 5 and by 2, because its last digit is 0.
1,275 is divisible by 5 (it ends in 5), but not by 2 and not by 10.
Class activity
“Digit cards”: the teacher writes the first two digits of a 3-digit number and pupils choose the last digit. For example, 47_ must be divisible by 5: which digits work? Teams try to find all correct options.
Practice
1
Which of 3,450, 1,275, 842, 3,007 are divisible by 5?
3,450 and 1,275
2
Which last digit makes 47* divisible by both 2 and 5?
0
3
120 pencils are packed 10 to a box. How many boxes are needed?
12
4
Why is every number divisible by 10 also divisible by 2 and by 5?
10 = 2 · 5. A number ending in 0 is even and also ends in 0, which is allowed for 5.