What is meant by the Term Factor?
A factor of a number is an integer that divides the number evenly, that is, there is no remainder after the division operation. The factors of a number can be determined using divisibility rules and division facts. Here, we will learn about the factors, prime factors, and factor pairs of 3.
What are the Factors of 3?
The factors of 3 are those integers that divide 3 without leaving any remainder. In other words, we can say that the factors of 3 will divide it evenly.
The factors of 3 can be positive as well as negative, but they cannot be decimals or fractions. The quotient obtained by dividing 3 by its factor is also a factor of 3.
The Factors of 3
Factors | Factor Pairs | Prime Factors |
|---|---|---|
1, 3 | (1, 3) | 3 |
For example, 3 is a factor of 3 because when 3 is divided by 3, it leaves 0 as the remainder and 1 as the quotient, which is also a factor of 3.
Factor List for the Number 3
Divisibility rules and division facts can be used to determine the factors of 3.
Divisor | Is the number a factor of 3? | Multiplication Equation |
|---|---|---|
1 | Yes, 1 is a factor of every number | 1 × 3 = 3 |
2 | No, 3 is odd. | - |
3 | Yes, 3 + 0 = 3, 3 is divisible by 3 | 3 × 1 = 3 |
The Prime Factors of 3
A factor tree can be used to determine the prime factors of 3, as shown in the figure.
From the factor tree, we can see that the factorization of 3 is 1 \(\times\) 3.
This means that 3 is the only prime factor of 3.
Read More:
The Factor Pairs of 3
The factor pair of any number is a set of two integers that, when multiplied, result in that number itself. So, the two integers are the factors of the number. A factor pair can be negative or positive.
[Note: The product of two negative numbers is positive.]
The factor pair of 3 is the set of two factors of 3 that, when multiplied, give 3 as the product.
Thus, the factor pairs of 3 can be obtained from the list of its factors.
Positive Factors of 3 | Positive Factor Pairs of 3 |
|---|---|
1 \(\times\) 3 | (1, 3) |
Rapid Recall
Solved Factors of 3 Examples
Example 1: Ingrid needs to climb three hills in 3 hours. If she spends an equal amount of time climbing each hill, what is the time taken to climb one hill?
Solution:
To find out the time taken to climb one hill, we will divide 3 by 3, that is,
\(\frac{3}{3}\)
= 1 [as (1, 3) is a factor pair of 3]
As a result, Ingrid spends one hour climbing each hill.
Example 2: Find the common factors of 17 and 3.
Solution:
The factors of 17: 1 and 17
The factors of 3: 1 and 3
So, the common factor of 3 and 17 is 1.
Hence, 17 and 3 have only one common factor.
Example 3: What are the common factors of 3 and 6?
Solution:
The factors of 3 are 1 and 3
The factors of 6 are 1, 2, 3, and 6
So, the common factors of 3 and 6 are 1 and 3.
Yes, 1 is a factor of 3. This is because the number 1 divides 3 exactly, that is, it leaves 0 as the remainder. So, 1 is a factor of 3. Also, 1 is a factor of every other natural number.
3 is not a composite number as it has exactly two factors. The factors of 3 are 1 and 3. This suggests that it is a prime number.
The factors of 3 are 1 and 3.
So, the smallest factor of 3 is 1, and the greatest factor is 3 itself.
The factors of 3 are 1 and 3.
Hence, the sum of all the factors of 3 is
= 1 + 3
= 4
Hence, the sum is 4.
The factors of 3 are 1, 3. So, 3 has two factors.