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Factors of 32 are the integers that can be evenly divided into 32. Factors of 32 are the numbers that can evenly divide the number 32. If a number divides 32 completely leaving zero as the remainder, then, that number is a factor of 32. There are six factors of 32, which are 1, 2, 4, 8, 16, and 32. 1 is the smallest whereas 32 is the largest factor of 32. The sum of all the factors of 32 is 63. The prime factorization of 32 is 2 x 2 x 2 x 2 x 2 or 25. The factors of 32 in pairs are (1, 32), (2, 16), and (4, 8). The pair factors result in the original number on multiplication with each other.
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Key Terms: Factors of 32, Prime Factors, Prime Factorization, Division, Pair Factors, Remainder, Composite Number, Multiplication
What are Factors of 32?
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A factor of a number refers to that number that divides it completely without any remainder. 32 is an even composite number. It means that it has more than two factors. The factors of 32 are all those integers that divide 32 without any remainder. The factors of 32 are 1, 2, 4, 8, 16, and 32.
Factors of 32: 1, 2, 4, 8, 16, and 32
Factors of 32
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| Relevant Concepts | ||
|---|---|---|
| Factors of 25 | Factors of 12 | Factors of 28 |
| Factors of 16 | Factors of 18 | Factors of 24 |
| Factors of 48 | Factors of 72 | Factors of 15 |
Factors of 32 in Pairs
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Two numbers that, when multiplied, give 32 are known as the factors of 32 in pairs. The pair factors of 32 are as follows:
| Positive Pair Factors | Negative Pair Factors |
|---|---|
| 1 × 32 = 32 (1, 32) | -1 × -32 = 32 (-1, -32) |
| 2 × 16 = 32 (2, 16) | -2 × -16 = 32 (-2, -16) |
| 4 × 8 = 32 (4, 8) | -4 × -8 = 32 (-4, -8) |
The pair factors of 32 can be negative too as seen in the table above. It is so because if we multiply the negative pair factors, we will still get the positive value of 32 on multiplication.
How to Calculate Factors of 32?
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In order to find out all the factors of 32, we need to divide the integer 32 by all the natural numbers from 1 to 32. The numbers that divide 32 are the factors of 32.
Step 1: We know that any natural number is also a factor of itself, thus,
32 ÷ 1 = 32
Step 2: 32 is an even number, thus, it is divisible by 2, so we will proceed with the same,
32 ÷ 2 = 16
Step 3: Checking it with other even numbers,
- 32 ÷ 4 = 8
- 32 ÷ 8 = 4
- 32 ÷ 16 = 2
- 32 ÷ 32 = 1
Thus, there are total six factors of 32 which are 1, 2, 4, 8, 16, and 32.
Read More: Twin Primes
Prime Factors of 32
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32 is a composite number which means that it has prime factors. We can calculate the prime factors of 32 with the help of the following steps:
Prime Factorization of 32
Step 1: To get the prime factorization of 32, divide the number 32 by the smallest prime factor, say 2.
32 ÷ 2 = 16
Step 2: Divide 16 by 2 and continue the process:
16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
2 ÷ 2 = 1
We have received the number 1 at the end of the division which means that we cannot proceed further. Thus, the prime factors of 32 are written as 2 × 2 x 2 x 2 x 2 or 25, where 2 is a prime number.
Read More: Prime Number Formula
Solved Examples on Factors of 32
Example 1: There are 32 toffees with Raveena that are to be distributed among 4 students in a class. Will each student get an equal number of toffees? How many toffees will each student get?
Solution: It is given that,
- Number of toffees = 32
- Number of students = 4
We know that 4 is a factor of 32. It means that it would divide it completely. Thus, yes, each student will get an equal number of toffees.
32/4 = 8
Thus, each student will get 8 toffees.
Example 2: What is the Greatest Common Factor of 32 and 14?
Solution: The factors of 32 and 14 are:
- Factors of 32: 1, 2, 4, 8, 16, 32
- Factors of 14: 1, 2, 7, 14
The common factors of 32 and 14 are 1 and 2. Thus, the greatest common factor of 32 and 14 is 2.
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| Related Topics | ||
|---|---|---|
| Relation Between HCF and LCM | Addition and Subtraction of Integers | LCM of Two Numbers |
| Digits | Greatest Common Divisor | Real Numbers |
Things to Remember
- Factors of 32 are the numbers that divide 32 completely leaving zero as the remainder.
- 1, 2, 4, 8, 16, and 32 are factors of 32.
- There are 3 pair factors of 32 which are (1, 32), (2, 16), and (4, 8).
- Factors of 32 can be calculated using the division method and prime factorization.
- The prime factorization of 32 is 2 x 2 x 2 x 2 x 2 with 2 as the only prime factor of 32.
- The sum of all the factors of 32 is 63.
Sample Questions
Ques. Write down the common factors of 32 and 64. (2 Marks)
Ans. Writing down all the factors of 32 and 64,
- Factors of 32 are 1, 2, 4, 8, 16, and 32.
- Factors of 64 are 1, 2, 4, 8, 16, 32, and 64.
Thus the common factors of 32 and 64 are 1, 2, 4, 8, 16, and 32.
Ques. There are 16 apples in one box and there are 2 boxes. Find out how many total apples are there in the boxes. (2 Marks)
Ans. It is given that,
- Apples in each box = 16
- Number of boxes = 2
Thus, the total number of apples would be 16 x 2 = 32.
Ques. What is the product of all the prime factors of 32? (2 Marks)
Ans. Prime Factors are those factors of a number that are prime numbers in nature. There is only one prime factor of 32 which is 2. Thus, the product of the prime factors of 32 is 2 only.
Ques. Anjali’s mother bakes 32 cookies. She puts 8 plates on the table. How many cookies would be there in each plate? (2 Marks)
Ans. According to the question,
____ × 8 = 32
We can clearly see that the missing factor is 4. Thus, her mom will distribute 32 cookies evenly as 32 ÷ 8 = 4.
Ques. What are the common factors of 32 and 20? (2 Marks)
Ans. We know that
- Factors of 32: 1, 2, 4, 8, 16, 32
- Factors of 20: 1, 2, 4, 5, 10, 20
Thus, 1, 2, and 4 are the common factors of 32 and 20.
Ques. What is the Sum of the Factors of 32? (2 Marks)
Ans. All the factors of 32 are 1, 2, 4, 8, 16, and 32.
Adding all of the given factors, we get
1 + 2 + 4 + 8 + 16 + 32 = 63.
Thus, the sum of the factors of 32 is 63.
Ques. How many factors does 32 have? (1 Mark)
Ans. 32 is an even composite number that indicates that it has more than 2 factors. There are 6 factors of 32 in total which are 1, 2, 4, 8, 16 and 32.
Ques. Are multiples and factors of 32 the same? (2 Marks)
Ans. No, the multiples and factors of 32 are different and not the same. Factors of 32 are finite but multiples of 32 can be determined indefinitely.
- There are only six factors of 32 that are 1, 2, 4, 8, 16, and 32.
- There are infinite multiples of 32 such as 32, 64, 96, 128, 160, 192, …..etc.
Ques. What are the multiples of 32? List the first 10 multiples of 32. (3 Marks)
Ans. Multiples of 32 are the product of the number 32 and an integer. The first 10 multiples of 32 are
- 32× 1 = 32
- 32 × 2 = 64
- 32 × 3 = 96
- 32 × 4 = 128
- 32 × 5 = 160
- 32 × 6 = 192
- 32 ×7 = 224
- 32 × 8 = 256
- 32 × 9 = 288
- 32 × 10 = 320
Thus, the first 10 multiples of 32 are 32, 64, 96, 128, 160, 192, 224, 256, 288 and 320.
Ques. What are the common factors of 32, 42, and 36? (2 Marks)
Ans. First, we will write down all the factors of all the numbers.
- Factors of 32: 1, 2, 4, 8, 16, 32
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
Thus, there are only 2 common factors of 32, 42 and 36 which are 1 and 2.
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