# Factors of 9972

Factors of 9972 are 1, 2, 3, 4, 6, 9, 12, 18, 36, 277, 554, 831, 1108, 1662, 2493, 3324, 4986, and 9972

#### How to find factors of a number

 1.   Find factors of 9972 using Division Method 2.   Find factors of 9972 using Prime Factorization 3.   Find factors of 9972 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 9972

• Divide 9972 by 1: 9972 ÷ 1 : Remainder = 0
• Divide 9972 by 2: 9972 ÷ 2 : Remainder = 0
• Divide 9972 by 3: 9972 ÷ 3 : Remainder = 0
• Divide 9972 by 4: 9972 ÷ 4 : Remainder = 0
• Divide 9972 by 6: 9972 ÷ 6 : Remainder = 0
• Divide 9972 by 9: 9972 ÷ 9 : Remainder = 0
• Divide 9972 by 12: 9972 ÷ 12 : Remainder = 0
• Divide 9972 by 18: 9972 ÷ 18 : Remainder = 0
• Divide 9972 by 36: 9972 ÷ 36 : Remainder = 0
• Divide 9972 by 277: 9972 ÷ 277 : Remainder = 0
• Divide 9972 by 554: 9972 ÷ 554 : Remainder = 0
• Divide 9972 by 831: 9972 ÷ 831 : Remainder = 0
• Divide 9972 by 1108: 9972 ÷ 1108 : Remainder = 0
• Divide 9972 by 1662: 9972 ÷ 1662 : Remainder = 0
• Divide 9972 by 2493: 9972 ÷ 2493 : Remainder = 0
• Divide 9972 by 3324: 9972 ÷ 3324 : Remainder = 0
• Divide 9972 by 4986: 9972 ÷ 4986 : Remainder = 0
• Divide 9972 by 9972: 9972 ÷ 9972 : Remainder = 0

Hence, Factors of 9972 are 1, 2, 3, 4, 6, 9, 12, 18, 36, 277, 554, 831, 1108, 1662, 2493, 3324, 4986, and 9972

#### 2. Steps to find factors of 9972 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 9972 using the division method, follow these steps:

• Step 1. Start dividing 9972 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 9972, which is 2. Divide 9972 by 2 to obtain the quotient (4986).
9972 ÷ 2 = 4986
• Step 3. Repeat step 1 with the obtained quotient (4986).
4986 ÷ 2 = 2493
2493 ÷ 3 = 831
831 ÷ 3 = 277
277 ÷ 277 = 1

So, the prime factorization of 9972 is, 9972 = 2 x 2 x 3 x 3 x 277.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 9972 as shown below:

So, the prime factorization of 9972 is, 9972 = 2 x 2 x 3 x 3 x 277.

#### 3. Find factors of 9972 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 9972 would be the two numbers which, when multiplied, give 9972 as the result.

The following table represents the calculation of factors of 9972 in pairs:

Factor Pair Pair Factorization
1 and 9972 1 x 9972 = 9972
2 and 4986 2 x 4986 = 9972
3 and 3324 3 x 3324 = 9972
4 and 2493 4 x 2493 = 9972
6 and 1662 6 x 1662 = 9972
9 and 1108 9 x 1108 = 9972
12 and 831 12 x 831 = 9972
18 and 554 18 x 554 = 9972
36 and 277 36 x 277 = 9972

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 9972. They are called negative pair factors.

Hence, the negative pairs of 9972 would be ( -1 , -9972 ) , ( -2 , -4986 ) , ( -3 , -3324 ) , ( -4 , -2493 ) , ( -6 , -1662 ) , ( -9 , -1108 ) , ( -12 , -831 ) , ( -18 , -554 ) and ( -36 , -277 ) .

#### How do you explain factors?

In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 9972 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 9972.
• Every number is a factor of zero (0), since 9972 x 0 = 0.
• 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, 4, 6, 9, 12, 18, 36, 277, 554, 831, 1108, 1662, 2493, 3324, 4986, 9972 are exact divisors of 9972.
• Factors of 9972 are 1, 2, 3, 4, 6, 9, 12, 18, 36, 277, 554, 831, 1108, 1662, 2493, 3324, 4986, 9972. Each factor divides 9972 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 9, 12, 18, 36, 277, 554, 831, 1108, 1662, 2493, 3324, 4986, 9972 are all less than or equal to 9972.

• Which is the smallest prime factor of 9972?

Smallest prime factor of 9972 is 2.

• Is 9972 a perfect square?

No 9972 is not a perfect square.

• What are five multiples of 9972?

First five multiples of 9972 are 19944, 29916, 39888, 49860, 59832.

• What is prime factorization of 9972?

Prime factorization of 9972 is 2 x 2 x 3 x 3 x 277.

• What are factors of 9972?

Factors of 9972 are 1, 2, 3, 4, 6, 9, 12, 18, 36, 277, 554, 831, 1108, 1662, 2493, 3324, 4986, 9972.

• How do you find factors of a negative number? ( eg. -9972 )?

Factors of -9972 are -1, -2, -3, -4, -6, -9, -12, -18, -36, -277, -554, -831, -1108, -1662, -2493, -3324, -4986, -9972.

• Is 9972 a whole number?

Yes 9972 is a whole number.

• Which is greatest factor of 9972?

The greatest factor of 9972 is 4986.

• What are the prime factors of 9972?

The factors of 9972 are 1, 2, 3, 4, 6, 9, 12, 18, 36, 277, 554, 831, 1108, 1662, 2493, 3324, 4986, 9972.
Prime factors of 9972 are 2, 2, 3, 3, 277.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 9972. Can you help her?

Prime factors of 9972 are 2, 2, 3, 3, 277.
Hence, the product of prime factors of 1662.

Can you help Rubel to find out the product of the even factors of 9972?

Factors of 9972 are 1, 2, 3, 4, 6, 9, 12, 18, 36, 277, 554, 831, 1108, 1662, 2493, 3324, 4986, 9972.
Even factors of 9972 are 2, 4, 6, 12, 18, 36, 554, 1108, 1662, 3324, 4986, 9972.
Hence, product of even factors of 9972 is; 2 x 4 x 6 x 12 x 18 x 36 x 554 x 1108 x 1662 x 3324 x 4986 x 9972 = 6.293229836038092e+25.

Joy wants to calculate mean of all the factors of 9972. Help him in finding the mean of 9972.

Factors of 9972 are 1, 2, 3, 4, 6, 9, 12, 18, 36, 277, 554, 831, 1108, 1662, 2493, 3324, 4986, 9972.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 9972 is 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 36 + 277 + 554 + 831 + 1108 + 1662 + 2493 + 3324 + 4986 + 9972 = 25298.
Hence, the mean of factors of 9972 is 25298 ÷ 18 = 1405.44.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 9972? Help her in writing all the factors.

Positive factors are 1, 2, 3, 4, 6, 9, 12, 18, 36, 277, 554, 831, 1108, 1662, 2493, 3324, 4986, 9972.
Negative factors are -1, -2, -3, -4, -6, -9, -12, -18, -36, -277, -554, -831, -1108, -1662, -2493, -3324, -4986, -9972.

How many factors are there for 9972?

Factors of 9972 are 1, 2, 3, 4, 6, 9, 12, 18, 36, 277, 554, 831, 1108, 1662, 2493, 3324, 4986, 9972.
So there are in total 18 factors.

Joey wants to write all the prime factors of 9972 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 9972 are 2, 2, 3, 3, 277.
So in exponential form it can be written as 22 x 32 x 277.

Kevin has been asked to write 17 factor(s) of 9972. Can you predict the answer?

17 factor(s) of 9972 are 1, 2, 3, 4, 6, 9, 12, 18, 36, 277, 554, 831, 1108, 1662, 2493, 3324, 4986.