Factors of 9999

Factors of 9999 are the numbers that get multiplied and produce the result as 9999. We can identify the factors of 9999 in multiple ways. Suppose by multiplying 4 and 3, and we get 12, i.e. 4 × 3 = 12 such that 4 and 3 are the factors of 12. Here, (4, 3) is called one of the positive factor pairs of 12. In the same way, we can find the factors of the number 9999. We know that finding the factors for large numbers such as 9999 is not simple as it is challenging to identify the numbers which produce 9999 through multiplication. In this article, you will learn what the factors of 9999 are, how to find the factors of a number 9999 in pairs using different methods and prime factors of 9999 with detailed steps.

The list of all factors of 9999, factor pairs and the prime factors 9999 are tabulated below:

Let’s learn how to find all the factors, pairs of factors and the prime factors of 9999.

What are the Factors of 9999?

Also, we know that the factors for 9999 are called the exact divisors of that number. That means the factor 9999 divides the number evenly. As we know, the number 9999 is a composite number, it has more than two factors, which means it has factors other than 1 and 9999.

How to Find the Factors of 9999?

Factors of any given number can be identified using two methods, namely multiplication and division.

Go through the steps given below to understand the process of finding the factors of 9999 by multiplication.

Step 1: First, write the number 9999 in your notebook.

Step 2: We know 1, and the number itself will be the factors of the given number. So, find some other two numbers, which on multiplication gives 9999, suppose 3 and 3333, such as 3 × 3333 = 9999.

Here, 3 is a prime number, so it cannot be factored further.

Step 3: Now, let’s try with different combinations of numbers in multiplication that produce the result as 9999, such as

9 × 1111 = 9999

11 × 909 = 9999

33 × 303 = 9999

99 × 101 = 9999

Step 4: Therefore, factors of 9999 are: 1, 3, 9, 11, 33, 99, 101, 303, 909, 1111, 3333 and 9999.

Factors of 9999 by Division Method

As mentioned above, factors are the exact divisors of the numbers. We know that the factors of odd numbers are also the odd numbers. So, we will be checking with only odd numbers in this division method.

9999 ÷ 1 = 9999 {remainder = 0; 1 and 9999 are factors}

9999 ÷ 3 = 3333 {remainder = 0; 3 and 3333 are factors}

9999 ÷ 5 = 1999.8 {remainder ≠ 0; not an exact divisor}

9999 ÷ 7 = 1428.428 {remainder ≠ 0; not an exact divisor}

9999 ÷ 9 = 1111 {remainder = 0; 9 and 1111 are factors}

9999 ÷ 11 = 909 {remainder = 0; 11 and 909 are factors}

…

9999 ÷ 101 = 99

Thus, the factors of 9999 are: 1, 3, 9, 11, 33, 99, 101, 303, 909, 1111, 3333 and 9999

Factors of 9999 in Pairs

To identify the pair factors of 9999, multiply the 2 numbers in a pair to have the original number as 9999. Also, the factors of any number can be both positive and negative. So, we can find both positive and negative factors of 9999 as given below:

If (p, q) is the factor pair of a number M, then (q, p) is also its factor pair.

The positive pair factors of 9999 are (1, 9999), (3, 3333), (9, 1111), (11, 909), (33, 303), (99, 101).

The negative pair factors of 9999 are (-1, -9999), (-3, -3333), (-9, -1111), (-11, -909), (-33, -303), (-99, -101).

Facts on Factors of 9999

Some important facts about the factors of 999 are listed below.

• The total number of factors of 9999 is 12.
• The sum of factors of 9999 is 15912.
• As 9999 is an odd number, it has only odd factors.

Prime Factorisation of 9999

By the prime factorization method, we can write the prime factors of 9999 as given below.

Step 1: The first step is to divide the number 9999 with the smallest prime number, i.e. 2.

9999 ÷ 2 = 4999.5

As we know, the factor cannot be a fraction; therefore, 2 is not the prime factor for 9999. So proceed to the next prime numbers, i.e. 3, 5, 7 and so on.

9999 ÷ 3 = 3333

Here 3 is the prime factor.

Step 2: Now, we divide 3333 by prime numbers.

3333 ÷ 2 = 1666.5

3333 ÷ 3 = 1111

Here 3 is again a prime factor.

Step 3: Let’s proceed with 1111.

1111 ÷ 2 = 555.5

1111 ÷ 3 = 370.33

1111 ÷ 5 = 222.2

1111 ÷ 7 = 158.714

1111 ÷ 11 = 101

Here,11 and 101 are prime numbers and hence, we cannot proceed with the division method.

Hence, the prime factorisation of 9999 can be expressed as 3 × 3 × 11 × 101 or 3² × 11 × 101.

Relation between factors and prime factors of 9999 is:

The exponents in the prime factorisation of 9999 are 2, 1 and 1. By adding one to each and multiplying them we get, (2 + 1)(1 + 1)(1 + 1) = 3 × 2 × 2 = 12. Thus, 9999 has exactly 12 factors. That means we can find the total number of factors of a number using the exponents of numbers in the prime factorisation of that number.

Video Lesson on Prime Factors

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