2
Divisors and multiples of a number
Textbook, pp. 6–9
GoalUnderstand divisor and multiple; list all divisors and the first multiples of a number.
New words
divisor · bo‘luvchimultiple · karralidivision with no remainder · qoldiqsiz bo‘linishnatural number · natural son
Explanation
If a natural number a is divisible by a natural number b with no remainder, then b is a divisor of a and a is a multiple of b. For example, 20 : 4 = 5 exactly, so 4 is a divisor of 20 and 20 is a multiple of 4. The smallest divisor of any number is 1 and the largest is the number itself. A number has infinitely many multiples, and the smallest is the number itself. To find divisors, try dividing by 1, 2, 3, ... in turn and write down the pairs.
Worked examples
Divisors of 12: 12 = 1 · 12 = 2 · 6 = 3 · 4, so 1, 2, 3, 4, 6, 12 (6 divisors in all).
Multiples of 7: 7, 14, 21, 28, 35, ... We get them by multiplying 7 by 1, 2, 3, 4, 5, ...
Class activity
“Find the pairs”: each pupil gets a card with a number from 1 to 36. When the teacher says “divisor of 24!”, pupils whose number divides 24 stand up. Then repeat with “multiple of 6!”.
Practice
1
How many divisors does 18 have?
6
2
Find the fifth multiple of 9.
45
3
Is 56 a multiple of 8? Check.
Yes, 56 = 8 · 7, it divides with no remainder.
4
Why does a number have a limited number of divisors but infinitely many multiples?
A divisor cannot be bigger than the number itself, but multiples keep growing as we multiply.