What is a Factor?
A factor of a number is a natural number that divides it evenly leaving no remainder. In other words, a certain number can be obtained by multiplying a pair of its factors.
Consider the number 15, we can obtain the number 15 if we multiply 1 by 15 or by multiplying 3 by 5.
Division of 15 by 1, 3, 5 or 15 does not leave a remainder. That is because 1, 3, 5 and 15 are the factors of 15.
What is a Prime Number?
Prime numbers are numbers that have exactly two factors that are 1 and the number itself. Dividing a prime number by any number other than 1 and the number itself leaves a remainder.
Some examples of prime numbers are 2, 3, 5, 7, 11, 13, 17 and so on. The number 2 has only factors that are 1 and 2. Similarly, the number 3 has factors 1 and 3. The same rule can be applied to all prime numbers.
What is a Composite Number?
Composite numbers are numbers that have more than two factors. In other words, it is possible to divide a composite number by more than two natural numbers without leaving any remainder.
Every composite number can be expressed as the product of prime numbers. Some examples of composite numbers are 4, 6, 8, 9 and 12. The factors of 4 are 1, 2 and 4, and the factors of 6 are 1, 2, 3 and 6. Similarly, all composite numbers have more than two factors.
Factors of 91
As discussed earlier, the factors of 91 will be the numbers that divide 91 evenly, that is, leave no remainder. So they are 1, 7, 13 and 91.
Is 91 a Prime Number or a Composite Number?
From above, the factors of 91 are 1, 7, 13 and 91, that is, 91 has more than two factors. In other words 91 has factors other than 1 and 91 itself. So as per the definition of prime numbers, 91 is not a prime number in fact it is a composite number.
Solved Examples
Example 1: The cost of a notebook is 7 dollars and Robert has 91 dollars in his pocket. What is the maximum number of notebooks Robert can buy with this money?
Solution:
We can use the repetitive addition method to find the number of notebooks Robert can buy.
7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 = 91
There are 13 sevens that add up to 91, so Robert can buy a maximum of 13 notebooks with 91 dollars.
Example 2: The length and area of a rectangular plot are 13 meter and 91 square meter respectively. Find the width of a plot.
Solution:
A = l \( \times \) b Write the formula for area of rectangle
91 = 13 \( \times \) b Substitute 91 for A and 13 for l
\( \frac{91}{13} \) = b Divide each side by 13
7 = b Simplify
So, the width of the plot is 7 meter.
Example 3: Find the prime factors of 182.
Solution:
Use the factor tree method to find the prime factors of 182.
From the above,
182 = 2 \( \times \) 7 \( \times \) 13
So, the prime factors of 182 are 2, 7 and 13.
1 is neither prime nor composite number because 1 has only one factor, that is 1 itself.
Since factors of 91 are 1, 7, 13 and 91. The prime numbers among them are 7 and 13, so, the prime factors of 91 are 7 and 13.
The factors of 91 are 1, 7 , 13 and 91.
Since 0 and 1 are not prime numbers, 2 is the smallest prime number. The factors of 2 are 1 and 2.
0 and 1 are neither prime nor composite. The numbers 2 and 3 are prime numbers. So, the smallest composite number is 4. The factors of 4 are 1, 2 and 4.