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Factors of 16 are the numbers that when multiplied in pairs give the product as 16. In simpler terms, the numbers that divide 16 completely with zero as the remainder are the factors of 16. There are 5 factors of 16, which are 1, 2, 4, 8, and 16 itself. 1 is the smallest factor of 16 whereas 16 is the biggest factor itself. The sum total of all the factors of 16 is 31. The factors of 16 in pairs are (1, 16), (2, 8), and (4, 4). The prime factorization of 16 is 2 × 2 × 2 × 2 = 24. Thus, 2 is the only prime factor of 16.
In short, The Factors of 16 can be summarized as:
- Factors of 16: 1, 2, 4, 8 and 16
- Negative Factors of 16: -1, -2, -4, -8, -16
- Prime Factors of 16: 2
- Prime Factorization of 16: 2 × 2 × 2 × 2 = 24
- Sum of Factors of 16: 31
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Key Terms: Factors of 16, Pair Factors, Prime Factors, Composite Number, Prime Factorization, Division, Remainder, Number System, Prime Numbers
What are Factors of 16?
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Factors of 16 are the list of numbers that divide the number 16 completely without leaving any remainder. 16 is an even composite number, which means it has more than 2 factors apart from 1 and the number itself. This means that there are a total of 5 factors of 16.
| Factors of 16: 1, 2, 4, 8 and 16 |
- A number which divides some other number without leaving any remainder is known as the factor of that number.
- In this case, when we divide 16 by 2, it is can be seen to be completely divisible, leaving no remainder.
- Thus, 2 is a factor of 16. Likewise, 4 and 8 also leave no remainder, becoming the factors of 16 as well.
- Note that 1 and 16 are included mainly because any number multiplied by 1 is itself, and any number multiplied by 16 is itself times 16.
- Thus, the other factors of 16 can be found by finding pairs of numbers which multiply to 16, such as 2 and 8, or 4 and 4.
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| Chapter-Related Topics | ||
|---|---|---|
| Factors of 72 | Factors of 42 | Factors of 12 |
| Factors of 24 | Factors of 48 | Factors of 18 |
Factors of 16 in Pairs
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Pair Factors of 16 are the set of two numbers that when multiplied will give the number 16 as the product. The pair factors of 16 are calculated as:
- 1 × 16 = 16
- 2 × 8 = 16
- 4 × 4 = 16
So, the pair factors of 16 are (1, 16), (2, 8), and (4, 4).
The pair factors of 16 are both positive and negative as negative pair factors also result in the positive value of 16 on multiplication with each other.
| Positive Pair Factors | Negative Pair Factors |
|---|---|
| 1 × 16 = 16 ⇒ (1, 16) | -1 × -16 = 16 ⇒ (-1, -16) |
| 2 × 8 = 16 ⇒ (2, 8) | -2 × -8 = 16 ⇒ (-2, -8) |
| 4 × 4 = 16 ⇒ (4, 4) | -4 × -4 = 16 ⇒ (-4, -4) |
How to Calculate Factors of 16?
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The factors of 16 can be calculated using the steps given below:
- Step 1: Write down the number 16 as the first step.
- Step 2: Now, find out two numbers that give the result of 16 on multiplication. Let us take 2 and 8, such as 2 × 8 = 16.
- Step 3: As 2 is a prime number with only two factors, i.e., 1 and the number itself (1 and 2). So, we can not factorize it further.
- Step 4: Moving on to the next number 8, which is a composite number. So, it can be factorized further.
- Step 5: 8 can be further factored as 2 x 2 x 2.
Thus, the factorization of 16 is 16 = 2 × 2 × 2 × 2.
Factors of 16 by Division Method
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16 is a composite which means it has more than two factors. To calculate the factors of 16 by division method, follow the given steps:
First, divide the number 16 by the smallest prime number which is 2.
→ 16 ÷ 2 = 8
Divide 8 by 2 and continue the process,
→ 8 ÷ 2 = 4
→ 4 ÷ 2 = 2
→ 2 ÷ 2 = 1
At last, we have received the number 1 at the end of the division process and we cannot proceed further. Thus, the factors of 16 are 1, 2, 4, 8, and 16.
Factors of 16 by Prime Factorization
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Factors of 16 can be calculated by dividing 16 by prime numbers. The prime factors of 16 can be found by the division method or the factor tree method.
Prime Factorization of 16 by Division Method
We can calculate the factors of 16 through prime factorization. In the prime factorization of 16, we will divide 16 by the smallest prime number 2. If the given number is odd, we divide it by 3. We will keep on dividing till we get 1.
Here is the prime factorization of 16:
Prime Factorization of 16
Thus, the prime factorization of 16 is 2 × 2 × 2 x 2 or 24, with 2 as its only prime number.
Prime Factorization of 16 by the Factor Tree Method
The factor tree of 16 is as follows:
Factor Tree of 16
Read More: NCERT Solutions for Class 6 Maths Playing With Numbers
Factors in Math
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Some examples of factors include:
Factors of 36
1, 2, 3, 4, 6, 9, 12, 18, and 36
These factors of 36 are positive integers dividing 36 without leaving any remainder.
Factors of 24
1, 2, 3, 4, 6, 8, 12, and 24
The factors of a number are numbers dividing the given number completely and leaving no remainder.
Factors of 12
The factors of 12 are 1, 2, 3, 4, 6, and 12.
Factors of 18
The factors of 18 are 1, 2, 3, 6, 9, and 18.
Factors of 48
The factors of 48 are:
1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
Solved Example on Factors of 16
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Example 1: Find the common factor of 16 and 15.
Solution: First, the factors of 16 and 15 are as follows:
- Factors of 16: 1, 2, 4, 8, and 16.
- Factors of 15: 1, 3, 5, and 15.
We can see that there is only one common factor of 16 and 15 which is 1.
Example 2: What is the sum of all the factors of 16?
Solution: There are 5 factors of 16- 1, 2, 4, 8 and 16.
Now, adding up the factors,
1 + 2 + 4 + 8 + 16 = 3
Thus, the sum of the factors of 16 is 31.
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Things to Remember
- Factors of 16 are the numbers that divide the number 16 completely with no remainder.
- Factors of 16 are 1, 2, 4, 8, and 16.
- Pair factors of 16 are (1, 16), (2, 8), and (4, 4).
- The prime factorization of 16 is written as 2 × 2 × 2 x 2 or 24.
- 2 is the only prime factor of 16.
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Sample Questions
Ques. What are the common factors of 16 and 14? (2 Marks)
Ans. The factors of 16 and 14 are:
- Factors of 16: 1, 2, 4, 8, and 16
- Factors of 14: 1, 2, 7, and 14.
Thus, the common factors of 14 and 16 are 1 and 2.
Ques. Roomi wants to know about the positive pair factors of 26. Help Roomi to identify all the positive factor pairs of 16. (2 Marks)
Ans. The factor pairs of 16 are:
- 1 × 16 = 16
- 2 × 8 = 16
- 4 × 4 = 16
Thus, the positive factor pairs of 16 are (1,16), (2,8), and (4,4).
Ques. What are the prime factors of 16? Find the product of all the prime factors of 16. (1 Mark)
Ans. There is only one prime factor of 16 which is 2. Thus, the product of prime factors of 2 will also be 2 only.
Ques. Anjali wants to write down the factors of 24 for her homework and check if the numbers 24 and 16 have any common factors. Help her with the same. (3 Marks)
Ans. There are eight factors of 24 which are as follows:
- 24 ÷ 1 = 24
- 24 ÷ 2 = 12
- 24 ÷ 3 = 8
- 24 ÷ 4 = 6
- 24 ÷ 6 = 4
- 24 ÷ 8 = 3
- 24 ÷ 12 = 2
We can see that,
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, and 24
- Factors of 16: 1, 2, 4, 8, and 16.
Thus, 24 and 16 have 1, 2, 4, and 8 as common factors.
Ques. What are multiples of 16? List the first 50 multiples of 16. (3 Marks)
Ans. Multiples of 16 are the numbers we get when 16 is multiplied by an integer.
The first 50 multiples of 16 are 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 224, 240, 256, 272, 288, 304, 320, 336, 352, 368, 384, 400, 416, 432, 448, 464, 480, 496, 512, 528, 544, 560, 576, 592, 608, 624, 640, 656, 672, 688, 704, 720, 736, 752, 768, 784, and 800.
Ques. Name the Greatest Common Factor of 16 and 5. (3 Marks)
Ans. Writing down all the factors of 16 and 5, we get
- Factors of 16: 1, 2, 4, 8, 16
- Factors of 5: 1, 5. 16 and 5
There is only one common factor which is 1, so the greatest common divisor of 16 and 5 is 1. It also means that 16 and 5 are co-prime.
Ques. Are all the factors of 16 even? (1 Mark)
Ans. Even though 16 is an even composite number, all the factors of 16 are not even. All other factors of 16 are even numbers except 1.
Ques. State the reason if 16 is a composite number. (2 Marks)
Ans. Yes, 16 is a composite number. It is an even composite number. 16 has more than two factors. It has 3 more factors than 1 and the number itself. Thus, there are total 5 factors of 16 which are 1, 2, 4, 8, and 16.
Ques. What do you mean by prime numbers? (2 Marks)
Ans. Prime numbers are those numbers that cannot be factored with another number. Examples of prime numbers include 2, 3, 5, 7, 11, 13, and 17. A prime number is only divisible by 1 only and itself.
Ques. What are the properties of factors? (3 Marks)
Ans. The important properties of factors are:
The number of factors of a given number is finite.
- The factor of a number is always less than or equal to the given number and cannot be greater than that.
- Every number except 1 has at least two factors, 1 and the number itself.
- Division and multiplication are the two arithmetic operations that are used in finding the factors of a number.
Ques. What is the prime factorisation of 118724? (1 mark)
Ans. The prime factorisation of 118724 is = 2 × 2 × 67 × 443.
Ques. What are the prime factorizations of the values given below? (5 marks)
(i) 23356
(ii) 50034
Ans. (i) 23356
| Factors | Prime Factors |
|---|---|
| 23356 = 11678 × 2 | 2 |
| 11678 = 5839 × 2 | 2, 5839 |
Hence, the Prime Factorization of 23356 is = 2 × 2 × 5839
(ii) 50034
| Factors | Prime Factors |
|---|---|
| 50034 = 25017 × 2 | 2 |
| 25017 = 8339 × 3 | 3 |
| 8339 = 269 × 31 | 31, 269 |
Thus, the Prime Factorization of 23356 is = 2 × 3 × 31 × 269
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