Factors of 33 Using Prime factorization
What are the Factors of 33?
The factors of 33 are natural numbers that divide 33 without leaving any remainder, or in other words, the factors of 33 divide 33 evenly.
For example, 3 is a factor of 33 because when we divide 33 by 3, it gives us 11 as the quotient and 0 as the remainder.
When a number is divided by its factor, the quotient obtained is also a factor of the number. So after the division operation, the quotient 11 is also a factor of 33.
From this explanation we can deduce that in order to check if any number is a factor of 33 or not, we divide 33 by that number and verify whether the remainder is zero or not. If the remainder is zero then the number is a factor, otherwise it’s not.
Factors of 33
Factors | Factor Pairs | Prime factorization |
|---|---|---|
1, 3, 11, 33 | (1, 33), (3, 11) | 33 = 3 × 11 |
Factor List of 33
The factors of 33 can be obtained by applying divisibility rules and division facts.
Number | Is the number a factor of 33? | Multiplication Equation |
|---|---|---|
1 | Yes, 1 is a factor of every number | 1 x 33 = 33 |
2 | No, 33 is an odd number | - |
3 | Yes, 3 + 3 = 6 is divisible by 3 | 3 x 11 = 33 |
4 | No, 33 \(\div\) 4 = 8 Remainder =1 | - |
5 | No, ones place digit in 33 is neither 0 nor 5 | - |
6 | No, 33 is divisible by 3 but not an even number | - |
7 | No, 33 \(\div\) 7 = 4 Remainder = 5 | - |
8 | No, 33 \(\div\) 8 = 4 Remainder = 1 | - |
9 | No, 3 + 3 = 6 is not divisible by 9 | - |
10 | No, ones place digit in 33 is not 0 | - |
11 | Yes, 33 \(\div\) 11 = 3 Remainder = 0 | 11 x 3 = 33 |
We can stop the derivation of factors with this step because the multiplication equations start to repeat. So, the factors of 33 are the multiplicands of each multiplication equation. Since there are 2 multiplication equations with unique multiplicands, the number 33 has four factors, which are, 1, 3, 11 and 33.
Prime Factorization of 33
Prime factorization implies that we express a number as a product of prime numbers. The prime numbers multiplied here are known as the prime factors of that number.
The factor tree of 33 that is represented as an image describes the prime factorization of 33.
From the factor tree, we can see that the prime factorization of 33 is 3 × 11.
This means 3 and 11 are the prime factors of 33.
Read More:
Factor Pairs of 33
The factor pair of 33 is the set of two factors of 33, which when multiplied together, result in 33.
For example: (3, 11) is a factor pair of 33, since ‘3 x 11 = 33’.
Factors of 33 | Factor Pairs of 33 |
|---|---|
1 × 33 | (1, 33) |
3 × 11 | (3, 11) |
Rapid Recall
Solved Factors of 33 Examples
Example 1: Find the common factors of 55 and 33.
Solution:
Factors of 55: 1, 5, 11 and 55.
Factors of 33: 1, 3, 11 and 33.
So, the common factors of 55 and 33 are 1 and 11.
Example 2: Anne wants to share 33 chocolates among 4 of her friends. Is it possible to share the chocolates equally?
Solution:
Number of chocolates = 33
Number of friends = 4
For Anne to be able to share the chocolates equally among her friends, the number of chocolates should be evenly divisible by the number of friends.
But 4 is not a factor 33, that is, 33 is not evenly divisible by 4.
Therefore, Anne will not be able to share 33 chocolates equally among 4 friends.
Example 3: A school library has a collection of 33 books on the history of America. The books are to be arranged evenly on 3 shelves. How many books will be placed on each shelf?
Solution:
33 books are to be evenly arranged on 3 shelves.
To find out how many books can be placed on each shelf, we will divide 33 by 3, that is,
\(\frac{33}{3}\)
= \(\frac{11~\times~3}{3}\) [(11,3) is a factor pair of 33]
= 11 [Divide both the numerator and the denominator by 3]
As a result, 11 books can be placed on one shelf.
No, when you divide 33 by 9 it will give 6 as a remainder, that is, 9 does not divide 33 evenly.
Numbers that divide 33 evenly, that is, leave zero as the remainder, are known as factors of 33.
The factors of 33 are 1, 3, 11 and 33.
Hence, the sum of all the factors of 33 is
1 + 3 + 11 + 33 = 48
Hence, the sum is 48.
Yes, 33 is a composite number as it has factors other than 1 and itself. It has factors 3 and 11 other than 1 and 33.
The factors of 33 are 1, 3, 11 and 33.
So, the least factor of 33 is 1 and the greatest factor is 33 itself.