59
Divisors and multiples
Textbook: Part 2, lesson 59, pp. 63–65
GoalThe ideas of divisor and multiple: finding all divisors and multiples of a number.
New words
divisor · bo‘luvchimultiple · karrali sonexact division · qoldiqsiz bo‘linishfactor · ko‘paytuvchi
Explanation
18 divided by 6 leaves no remainder: 18 : 6 = 3. So 6 is called a divisor of 18, and 18 a multiple of 6. To find divisors quickly, split the number into pairs of factors: 12 = 1 × 12 = 2 × 6 = 3 × 4, so the divisors are 1, 2, 3, 4, 6, 12. To list multiples, multiply the number by 1, 2, 3, ...
Worked examples
Divisors of 18: 1, 2, 3, 6, 9, 18 (1 × 18, 2 × 9, 3 × 6).
The first multiples of 7: 7, 14, 21, 28, 35, 42.
Class activity
“Multiple or divisor”: the teacher says two numbers (for example 42 and 6). Children check and say “42 is a multiple of 6” or “6 is a divisor of 42”; if that is not possible they give the remainder.
Practice
1
Write all divisors of 24.
1, 2, 3, 4, 6, 8, 12, 24
2
Which of 28, 35, 42, 50, 63 are multiples of 7?
28, 35, 42 and 63 (50 : 7 = 7, remainder 1)
3
Write the first five multiples of 6.
6, 12, 18, 24, 30
4
How many divisors does 20 have?
6
5
Is 49 a multiple of 6? Why?
No: 49 : 6 = 8 (remainder 1), it does not divide exactly