# Factors of 1998

Factors of 1998 are 1, 2, 3, 6, 9, 18, 27, 37, 54, 74, 111, 222, 333, 666, 999, and 1998

#### How to find factors of a number

 1.   Find factors of 1998 using Division Method 2.   Find factors of 1998 using Prime Factorization 3.   Find factors of 1998 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 1998

• Divide 1998 by 1: 1998 ÷ 1 : Remainder = 0
• Divide 1998 by 2: 1998 ÷ 2 : Remainder = 0
• Divide 1998 by 3: 1998 ÷ 3 : Remainder = 0
• Divide 1998 by 6: 1998 ÷ 6 : Remainder = 0
• Divide 1998 by 9: 1998 ÷ 9 : Remainder = 0
• Divide 1998 by 18: 1998 ÷ 18 : Remainder = 0
• Divide 1998 by 27: 1998 ÷ 27 : Remainder = 0
• Divide 1998 by 37: 1998 ÷ 37 : Remainder = 0
• Divide 1998 by 54: 1998 ÷ 54 : Remainder = 0
• Divide 1998 by 74: 1998 ÷ 74 : Remainder = 0
• Divide 1998 by 111: 1998 ÷ 111 : Remainder = 0
• Divide 1998 by 222: 1998 ÷ 222 : Remainder = 0
• Divide 1998 by 333: 1998 ÷ 333 : Remainder = 0
• Divide 1998 by 666: 1998 ÷ 666 : Remainder = 0
• Divide 1998 by 999: 1998 ÷ 999 : Remainder = 0
• Divide 1998 by 1998: 1998 ÷ 1998 : Remainder = 0

Hence, Factors of 1998 are 1, 2, 3, 6, 9, 18, 27, 37, 54, 74, 111, 222, 333, 666, 999, and 1998

#### 2. Steps to find factors of 1998 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 1998 using the division method, follow these steps:

• Step 1. Start dividing 1998 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 1998, which is 2. Divide 1998 by 2 to obtain the quotient (999).
1998 ÷ 2 = 999
• Step 3. Repeat step 1 with the obtained quotient (999).
999 ÷ 3 = 333
333 ÷ 3 = 111
111 ÷ 3 = 37
37 ÷ 37 = 1

So, the prime factorization of 1998 is, 1998 = 2 x 3 x 3 x 3 x 37.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1998 as shown below:

So, the prime factorization of 1998 is, 1998 = 2 x 3 x 3 x 3 x 37.

#### 3. Find factors of 1998 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 1998 would be the two numbers which, when multiplied, give 1998 as the result.

The following table represents the calculation of factors of 1998 in pairs:

Factor Pair Pair Factorization
1 and 1998 1 x 1998 = 1998
2 and 999 2 x 999 = 1998
3 and 666 3 x 666 = 1998
6 and 333 6 x 333 = 1998
9 and 222 9 x 222 = 1998
18 and 111 18 x 111 = 1998
27 and 74 27 x 74 = 1998
37 and 54 37 x 54 = 1998

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 1998. They are called negative pair factors.

Hence, the negative pairs of 1998 would be ( -1 , -1998 ) , ( -2 , -999 ) , ( -3 , -666 ) , ( -6 , -333 ) , ( -9 , -222 ) , ( -18 , -111 ) , ( -27 , -74 ) and ( -37 , -54 ) .

#### What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 1998 is a factor of itself.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 2, 3, 6, 9, 18, 27, 37, 54, 74, 111, 222, 333, 666, 999, 1998 are exact divisors of 1998.
• 1 is a factor of every number. Eg. 1 is a factor of 1998.
• Every number is a factor of zero (0), since 1998 x 0 = 0.

• Which is the smallest prime factor of 1998?

Smallest prime factor of 1998 is 2.

• Is 1998 a perfect square?

No 1998 is not a perfect square.

• What are five multiples of 1998?

First five multiples of 1998 are 3996, 5994, 7992, 9990, 11988.

• What is prime factorization of 1998?

Prime factorization of 1998 is 2 x 3 x 3 x 3 x 37.

• What are factors of 1998?

Factors of 1998 are 1, 2, 3, 6, 9, 18, 27, 37, 54, 74, 111, 222, 333, 666, 999, 1998.

• How do you find factors of a negative number? ( eg. -1998 )?

Factors of -1998 are -1, -2, -3, -6, -9, -18, -27, -37, -54, -74, -111, -222, -333, -666, -999, -1998.

• Is 1998 a whole number?

Yes 1998 is a whole number.

• Which is greatest factor of 1998?

The greatest factor of 1998 is 999.

• What are the prime factors of 1998?

The factors of 1998 are 1, 2, 3, 6, 9, 18, 27, 37, 54, 74, 111, 222, 333, 666, 999, 1998.
Prime factors of 1998 are 2, 3, 3, 3, 37.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 1998. Can you help her?

Prime factors of 1998 are 2, 3, 3, 3, 37.
Hence, the product of prime factors of 222.

Can you help Rubel to find out the product of the even factors of 1998?

Factors of 1998 are 1, 2, 3, 6, 9, 18, 27, 37, 54, 74, 111, 222, 333, 666, 999, 1998.
Even factors of 1998 are 2, 6, 18, 54, 74, 222, 666, 1998.
Hence, product of even factors of 1998 is; 2 x 6 x 18 x 54 x 74 x 222 x 666 x 1998 = 254977534976256.

Joy wants to calculate mean of all the factors of 1998. Help him in finding the mean of 1998.

Factors of 1998 are 1, 2, 3, 6, 9, 18, 27, 37, 54, 74, 111, 222, 333, 666, 999, 1998.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 1998 is 1 + 2 + 3 + 6 + 9 + 18 + 27 + 37 + 54 + 74 + 111 + 222 + 333 + 666 + 999 + 1998 = 4560.
Hence, the mean of factors of 1998 is 4560 ÷ 16 = 285.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 1998? Help her in writing all the factors.

Positive factors are 1, 2, 3, 6, 9, 18, 27, 37, 54, 74, 111, 222, 333, 666, 999, 1998.
Negative factors are -1, -2, -3, -6, -9, -18, -27, -37, -54, -74, -111, -222, -333, -666, -999, -1998.

How many factors are there for 1998?

Factors of 1998 are 1, 2, 3, 6, 9, 18, 27, 37, 54, 74, 111, 222, 333, 666, 999, 1998.
So there are in total 16 factors.

Joey wants to write all the prime factors of 1998 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1998 are 2, 3, 3, 3, 37.
So in exponential form it can be written as 2 x 33 x 37.

Kevin has been asked to write 15 factor(s) of 1998. Can you predict the answer?

15 factor(s) of 1998 are 1, 2, 3, 6, 9, 18, 27, 37, 54, 74, 111, 222, 333, 666, 999.