Factors of 99 Using Prime Factorization
What are the Factors of 99?
The numbers that divide 99 completely, that is, without leaving any remainder, are known as factors of 99.
Factors of 99: 1, 3, 9, 11, 33 and 99.
Factors completely divide the number. As a result of this, they cannot be fractions or decimals. The method of prime factorization can be used to find the factors of 99.
Factors | Factor Pairs | Prime factorization |
|---|---|---|
1, 3, 9, 11, 33 and 99 | (1, 99), (3, 33) and (9, 11) | 99 = 3\(^2\) × 11 |
The factors of 99 are numbers that divide 99 without leaving any remainder.
For Example:
Dividing 99 by 9 yields a quotient of 11 and a remainder of 0, which means that 9 is a factor of 99. Also the quotient is also a factor of 99.
Divide a number by 99 to see if it is a factor of 99; if the remainder is zero, then the number is a factor of 99.
Prime Factorization of 99
99 is a composite number, that is, it has more than two factors. To carry out prime factorization of 99, we will keep dividing 99 by its prime factors, until we get the quotient as 1.
- The first step is to divide 99 by its smallest prime factor, which is 3, in this case.
99 ÷ 3 = 33
33 ÷ 3 = 11
- Now, we have to divide 11 by 11 to get the result as 1.
11 ÷ 11 = 1
Hence, the prime factorization of 99 is 3 x 3 x 11 = 3\(^2\) x 11 where 3 and 11 are prime numbers.
The factor tree of 99 can be written as:
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Factor Pairs of 99
When a pair of factors of 99 are multiplied together to result in 99, they are said to be factor pairs or pair factors of 99.
For example, (3, 33) is a factor pair of 99 because 3 × 33 = 99 and 3 and 33 are factors of 99.
Positive factors of 99 | Positive pair factors of 99 |
|---|---|
1 x 99 | (1, 99) |
3 x 33 | (3, 33) |
9 x 11 | (9, 11) |
Solved Factors of 99 Examples
Example 1: Find the number of common factors of 36 and 99.
Solution:
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 99: 1, 3, 9, 11, 33 and 99.
So, the common factors of 36 and 99 are 1, 3 and 9.
Hence, 36 and 99 have 3 common factors.
Example 2: Nathan has a collection of 99 toys. The toys are to be arranged evenly on 3 shelves. How many toys will he place on each shelf?
Solution:
99 toys are to be evenly arranged on 3 shelves.
To find how many toys can be placed on each shelf, we will divide 99 by 3, that is,
So, \(\frac{99}{3}=\frac{3\times 33}{3}=33\)
Hence, Nathan can place 33 toys on each shelf.
Example 3: Is 7 a factor of 99?
Solution:
\(\frac{99}{7}\) = 14R1
7 does not divide 99 exactly. It leaves a remainder of 1. So, 7 is not a factor of 99.
The factors of 99 are 1, 3, 9, 11, 33 and 99.
Sum of factors = 1 + 3 + 9 + 11 + 33 + 99 = 156
So, the sum of factors of 99 is 156.
Yes, because 99 has more than two factors. The factors of 99 are: 1, 3, 9, 11, 33 and 99. Therefore, 99 is a composite number.
The factors of 99 are 1, 3, 9, 11, 33 and 99.
So, the least factor of 99 is 1 and the greatest factor is 99 itself.
The following are some important properties of factors:
- An exact divisor of a number is called a factor.
- Every number has a factor of one.
- The greatest factor of a number is the number itself.
- A factor can never be greater than the number.