Factors of 66 Using Prime Factorization
- What are the Factors of 66?
- List of the Factors of 66
- Prime Factorization of 66
- Factor Pairs of 66
- Positive Factor Pairs of 66
- Rapid Recall
- Solved Examples
- Frequently Asked Questions
What are the Factors of 66?
If the number 66 is divided by a natural number such that the remainder is zero, the natural number is known as a factor of 66. Here, the quotient obtained on division is also a factor of 66.
The factors of 66 are 1, 2, 3, 6, 11, 22, 33, and 66 because all these numbers divide the number 66 evenly.
List of the Factors of 66
In the next part of this article we will apply divisibility rules and division facts to determine the factors of 66.
Number | Is the number a factor of 66? | Multiplication equation |
| 1 | Yes, 1 is a factor of every number. | 1 \(\times\) 66 = 66 |
2 | Yes, 66 is even. | 2 \(\times\) 33= 66 |
3 | Yes, 6 + 6 = 12 is divisible by 3. | 3 \(\times\) 22= 66 |
4 | No, 66 \(\div\) 4 = 16 R2 | – |
5 | No, ones place digit is neither 0 nor 5. | – |
6 | Yes, 66 is even and divisible by 3. | 6 \(\times\) 11= 66 |
7 | No, 66 \(\div\) 7 = 9 R3 | – |
8 | No, 66 \(\div\) 8 = 8 R2 | – |
9 | No, 66 \(\div\) 9 = 7 R3 | – |
We can stop after checking for 9 because the factor pairs start to repeat.
So, the factors of 66 are 1, 2, 3, 6, 11, 22, 33, and 66.
[Note: In order to check whether a number is a factor of 66 or not, divide 66 by that number and check the remainder value. If the remainder is zero then the number is a factor of 66 otherwise not.]
Prime Factorization of 66
If a number can be expressed as a product of prime numbers, these prime numbers are known as the prime factors of that number. The process of writing this multiplication of prime factors is known as prime factorization.
The prime factorization of 66 can be represented by using a factor tree as shown below.
So, the prime factorization of 66 is \(66=2 \times 3 \times 11\), and the prime factors of 66 are 2, 3, and 11.
Factor Pairs of 66
A factor pair of a number is a set of two of any of its factors such that their product is the number itself. A factor pair can be a negative pair or a positive pair.
Factors pairs of a number can be obtained from the list of its factors.
For example (1, 66) is a factor pair of 66 as 1 x 66 = 66.
Positive Factor Pairs of 66
Positive Factors of 66 | Positive Factor Pairs of 66 |
1 \(\times\) 66 | (1, 66) |
2 \(\times\) 33 | (2, 33) |
3 \(\times\) 22 | (3, 22) |
6 \(\times\) 11 | (6, 11) |
Rapid Recall
The factors of 66 are 1, 2, 3, 6, 11, 22, 33, and 66.
Read More:
| factors of 36 | factors of 30 | factors of 63 | factors of 108 | factors of 8 |
| factors of 120 | factors of 42 | factors of 20 | factors of 54 | factors of 100 |
| factors of 72 | factors of 24 | factors of 96 | factors of 28 | factors of 180 |
| factors of 40 | factors of 84 | factors of 32 | factors of 56 | factors of 50 |
| factors of 90 | factors of 48 | factors of 45 | factors of 64 | factors of 35 |
Solved Factors of 66 Examples
Example 1: Find the common factors of 66 and 72.
Solution:
Factors of 66 = 1, 2, 3, 6, 11, 22, 33, and 66
Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72
Therefore, the common factors of 66 and 72 are 1, 2, 3, and 6.
Example 2: Find the greatest common factor of 66 and 78.
Solution:
Factors of 66 = 1, 2, 3, 6, 11, 22, 33, and 66
Factors of 78 = 1, 2, 3, 6, 13, 26, 39, and 78.
So, the common factors of 66 and 78 are 1, 2, 3, and 6.
Therefore, the greatest common factor of 66 and 78 is 6.
Example 3: Tom was studying geometrical shapes and found a rectangle of area 66 square centimeters. What are the possible dimensions of the base and height of the rectangle?
Solution :
The area of the rectangle is, 66 \(cm^2\).
Area of rectangle = l \(\times\) w where l is length and w is width.
66 = l \(\times\) w Given area of the rectangle is 66 sq.cm.
Since the product of length and width is 66, the possible dimensions of the rectangle can be determined from the factor pairs of 66.
Therefore, the possible dimensions of the rectangle are:
Length in centimeters | Width in centimeters |
| 1 | 66 |
2 | 33 |
3 | 22 |
6 | 11 |
11 | 6 |
22 | 3 |
33 | 2 |
66 | 1 |
Frequently Asked Questions on Factors of 66
A composite number is a number that has a factor other than 1 and itself, that is, a composite number has more than two factors.
The division of any number by 1 results in zero as the remainder, and the quotient is the number itself. Hence, 1 is a factor of all numbers.
Factors of 66 = 1, 2, 3, 6, 11, 22, 33, and 66.
Sum of factors of 66 = 1 + 2 + 3 + 6 + 11 + 22 + 33 + 66
= 144
5 is not a factor of 66 because the digit at the ones place is neither 0 nor 5. If we divide 66 by 5 then we get 13 as the quotient and 1 as the remainder.
