Factors of 18 Using Prime Factorization
What are the Factors of 18?
The integers that can divide a number exactly are known as factors of that number. When a number is divided by its factor the remainder is zero and the quotient is also a factor of that number.
The number 18 has a total of six factors: 1, 2, 3, 6, 9 and 18.
Factor list of 18
By applying the divisibility rules and division facts we can find the factors of 18.
Divisor | Is the number a factor of 18 | Multiplication equation |
|---|---|---|
1 | Yes, 1 is a factor of every number. | 1 x 18 = 18 |
2 | Yes, 18 is even. | 2 x 9 = 18 |
3 | Yes, 1 + 8 = 9 is divisible by 3. | 3 x 6 = 18 |
4 | No, 18 \(\div\) 4 = 4 R2 | - |
5 | No, 18 \(\div\) 5 = 3 R3 | - |
6 | Yes, 18 is even and divisible by 3. | 6 x 3 = 18 |
7 | No, 18 \(\div\) 7 = 2 R4 | - |
8 | No, 18 \(\div\) 8 = 2 R2 | - |
9 | Yes, 18 \(\div\) 9 = 2R0 | 9 x 2 = 18 |
Therefore, the factors of 18 are 1, 2, 3, 6, 9 and 18.
Prime Factorization of a Number
The factor tree below can be used to derive the prime factorization of 18:
Prime factorization of 18 is 2 × 3 × 3 = 2 × 3\(^2\)
Also, we can also say that 2 and 3 are the prime factors of 18.
Read More:
Positive Factor Pairs of 18
Pair factor or factor pair of 18 is a set of two factors of 18 which when multiplied give 18 as the product. For example, (1, 18) is a factor pair of 18, as both 1 and 18 are factors of 18 and 1 x 18 = 18.
Positive Factors of 18 | Positive Factor pairs of 18 |
|---|---|
1 x 18 | (1, 18) |
2 x 9 | (2, 9) |
3 x 6 | (3, 6) |
Solved Factors of 18 Examples
Example 1 :Find the common factors of 18 and 36.
Solution:
The factors of 18 are 1, 2, 3, 6, 9 and 18.
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36.
Hence, the common factors of 18 and 36 are 1, 2, 3, 6, 9 and 18.
Example 2: There are 4 hooks on a coat rack. 26 people want to hang their coats. It is known that it is possible to hang a maximum of two coats on one hook. The remaining coats are folded into 3 equal stacks and placed near the stand. How many coats are there in each stack?
Solution:
Number of people = 26
Number of hooks = 4
Two coats can be hung on a hook.
Therefore, total number of coats hung on the hooks = 2 x 4 = 8
Number of coats remaining = 26 – 8 = 18
The remaining coats are folded into 3 equal stacks,
Hence, the number of stacks = \(\frac{18}{3}=6\)
So, each stack will have 6 coats.
Example 3: Tracy goes to a florist. She wants to buy lilies, roses, orchids and tulips. She has 18 dollars with her. She spends an equal amount of money on each type of flower. With the money left with her, she buys herself a basket. What is the amount spent on the basket?
Solution:
Number of types of flowers = 4
Amount of money available = $ 18
Tracy spends an equal amount on each type of flower.
Therefore, amount spend on each type of flower = \(\frac{$~18}{4}\) = $4 R2
Total amount of money spend = $4 x 4 = $16
Amount of money left = $18 – $16 = $2
Therefore, she spends $2 on a basket.
Example 4: Find the common factors of 18 and 19?
Solution:
The factors of 18 are 1, 2, 3, 6, 9 and 18.
The factors of 19 are 1 and 19.
Hence, the common factors of 18 and 19 are only 1.
1, 2, 3, 6, 9 and 18 are the factors of 18.
2 × 3 × 3, is the prime factorization of 18.
(1, 18), (2, 9) and (3, 6) are the positive pair factors of 18.
Yes, 6 is a factor of 18 as 6 divides 18 exactly and leaves 0 as the remainder. Hence, 6 is a factor of 18.