Factors of 33
Factors of 33 are the list of integers that can be evenly divided into 33. There are 4 factors of 33, which are 1, 3, 11, and 33. Here, 33 is the biggest factor. The sum of all factors of 33 is 48. Its Prime Factors are 1, 3, 11, 33, and (1, 33) and (3, 11) are Pair Factors.
- Factors of 33: 1, 3, 11 and 33
- Negative Factors of 33: -1, -3, -11 and -33
- Prime Factors of 33: 3, 11
- Prime Factorization of 33: 3 × 11 = 3 × 11
- Sum of Factors of 33: 48
| 1. | What Are the Factors of 33? |
| 2. | How to Calculate Factors of 33? |
| 3. | Factors of 33 by Prime Factorization |
| 4. | Important Notes |
What are the Factors of 33?
The factors of 33 are all the numbers that give the value 33 when multiplied.
How to Calculate the Factors of 33?
Let's learn how to calculate the factors of 33
- Step 1: Write down the number to be factored i.e., 33.
- Step 2: Find the two numbers whose product gives 33.
As we know, 33 can be written as a product of 3 and 11. Here, 3 and 11 are both prime numbers. Thus, 3 can be written as, 3 = 3 × 1 and 11 can be written as, 11 = 11 × 1.
Hence, factors of 33 are 1, 3, 11, and 33.
Explore factors using illustrations and interactive examples
- Factors of 36 - The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 30 - The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
- Factors of 43 - The factors of 43 are 1, 43
- Factors of 32 - The factors of 32 are 1, 2, 4, 8, 16, 32
- Factors of 300 - The factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150
, 300 - Factors of 34 - The factors of 34 are 1, 2, 17, 34
Important Notes:
- 1 is the smallest factor of every number. Hence, it is one of the factors of 33.
- 33 is a multiple of 11. Hence, 11 is one of its factors.
Factors of 33 by Prime Factorization
Let's learn a bit about prime factorization before we learn how to find the factors of 33.
Let's learn how to find factors using prime factorization.
- Step 1: Write the pair of factors that give the required number when multiplied.
- Step 2: Check if the factors are prime.
- Step 3: Use the criteria given below for the factorization procedure.
The criteria for the factorization procedure is as follows:
- If both the numbers are prime, they can be multiplied as it is.
- If one among them is prime and the other number is composite, then the composite number is dissociated into its factors.
- If both the numbers are composite, each of them can be dissociated into factors.
These are the steps to find the factors of 33 using prime factorization:
- Step 1: 33 can be factored as a product of 3 and 11.
- Step 2: Check the factors to see if each one of them is prime or not.
3 is a prime number and can be dissociated as a product of 3 and 1.
11 is a prime number and can be dissociated as a product of 11 and 1. - Step 3: As per the criteria for factorization, both the numbers are prime and they can be multiplied as it is.
33 can thereby be written as 33 = 3 × 11. Thus, the prime factors of 33 are 3 and 11.
Factors of 33 in Pairs
The pair factors of 33 are:
| Factors | Pair factors |
|---|---|
| 1 × 33 | 1, 33 |
| 3 × 11 | 3, 11 |
| 11 × 3 | 11, 3 |
| 33 × 1 | 33, 1 |
The above-given factors are positive pair factors. It is possible to have negative pair factors as well because the product of two negative numbers gives a positive number.
Let's take a look at the negative pair factors.
| Factors | Pair factors |
|---|---|
| -1 × -33 | -1, -33 |
| -3 × -11 | -3, -11 |
| -11 × -3 | -11, -3 |
| -33 × -1 | -33, -1 |
Challenging Questions
- Mark takes 33 hours to travel from his home to Chicago by car. He stops after every 4 hours. How many stops will he make?
- How will Lamark distribute $33 into 2 parts such that each part gets an equal amount?
Factors of 33 Solved Examples
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Example 1: John owns an automobile repair shop. He has 33 customers who want all the tires of their cars to be replaced. If it takes him 3 hours to replace all the tires of one car, how much time will it take him to change the car tires for all his 33 customers?
Solution:
John can replace all the tires of a car in 3 hours. There are 33 customers, hence, there are 33 cars. The amount of time needed for John to replace the car tires for 33 cars will be given by,
33 × 3 = 99
Hence, John will need 99 hours to replace the car tires of those 33 customers
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Example 2: Adaline owns a jewelry store. Her store is known for its exquisite collection of diamond necklaces. Eleven customers placed an order for 33 necklaces to be made. How many necklaces were requested by each person assuming they ordered the same numbers each?
Solution:
Adaline has to make 33 necklaces as per the order given by the 11 customers. The number of orders placed by each person is,
33 ÷ 11 = 3
Each customer placed an order of 3 necklaces.
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Example 3: How many factors are there for 33?
Solution:
The factors of 33 are 1, 3, 11, 33. Therefore, 33 has 4 factors.
FAQs on Factors of 33
What are the Factors of 33?
The factors of 33 are 1, 3, 11, 33 and its negative factors are -1, -3, -11, -33.
What is the Sum of the Factors of 33?
Since all factors of 33 are 1, 3, 11, 33 therefore, the sum of its factors is 1 + 3 + 11 + 33 = 48.
What Numbers are the Prime Factors of 33?
The prime factors of 33 are 3, 11.
How Many Factors of 33 are also common to the Factors of 18?
Since, the factors of 33 are 1, 3, 11, 33 and the factors of 18 are 1, 2, 3, 6, 9, 18.
Hence, [1, 3] are the common factors of 33 and 18.
What is the Greatest Common Factor of 33 and 7?
The factors of 33 are 1, 3, 11, 33 and the factors of 7 are 1, 7. 33 and 7 have only one common factor which is 1. This implies that 33 and 7 are co-prime.
Hence, the Greatest Common Factor (GCF) of 33 and 7 is 1.
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