## Math 6 Chapter 1 Lesson 13: Divisors and Multiples

## 1. Summary of theory Tóm

### 1.1. Wish and multiple.

If 18 is divisible by 3, then 18 is a multiple of 3 and 3 is a divisor of 18.

If there is a natural number a that is divisible by b, then we say that a is a multiple of b, and b is called a divisor of a.

### 1.2. How to find divisors and multiples.

We denote the set of divisors of a la U{a}, the set of multiples of a as B{a}.

**VD1: **Find multiples less than 30 of 7.

Multiply 7 by 0, 1, 2, 3, 4 in turn, we get the multiples less than 30 of 7 which are 0, 7, 14, 28.

We can find multiples of a non-zero number by multiplying that number by 0, 1, 2, 3, ….

**VD2: **Find the set U{8}.

Divide 8 by 1, 2, 3, 4, 6, 7, 8 in turn, we see that 8 is only divisible by 1, 2, 4, 8.

Therefore: U{8} = {1, 2, 4, 8}.

We can find the divisors of a ( a > 1) by dividing a by the natural numbers 1 through a in turn to see which numbers a is divisible by, then those numbers are divisors of a.

## 2. Illustrated exercise

**Question 1: **Write the elements of the set U{9}.

**Solution guide:**

U{9} = {1, 3, 9}.

**Verse 2: **Find multiples less than 40 of 8.

**Solution guide:**

Multiples less than 40 of 8 are: 0, 8, 16, 24, 32.

**Question 3: **Find the divisors of 4.

**Solution guide:**

U{4} = {1, 2, 4}.

## 3. Practice

### 3.1. Essay exercises

**Question 1: **Write the elements of the set U{8}.

**Verse 2: **Find multiples less than 50 of 6.

**Question 3:** Find the divisors of 5.

### 3.2. Multiple choice exercises Bài

**Question 1: **Find multiples of 3 of the following numbers: 18, 33, 35, 40.

A. 18, 33

B. 18, 35

C. 18, 40

D. 35, 40

**Verse 2: **The natural numbers \(x\) satisfying : \(x\) \(\vdots\) \(12\) and \(20 \leq x \leq 40\) are :

A. 12, 24

B. 24, 36

C. 12, 48

D. 36, 48

**Question 3: **Find the set U{5} ?

A. U{5} = {1, 5}

B. U{5} = {5, 10}

C. U{5} = {0, 5}

D. U{5} = {0, 1}

**Question 4: **If the natural number a is divisible by the natural number b, then ?

A. a is the divisor of b.

B. a is a multiple of b.

C. b is a multiple of a.

D. a is the child of b.

**Question 5: **Multiples of 5 less than 20 are:

A. 1.5

B. 0, 5, 10, 15

C. 0, 3, 5

D. 3, 5, 7

## 4. Conclusion

Through this lesson on Divisors and Multiples, you need to accomplish some of the objectives given by the lesson, such as:

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