# Factors of 3969

Factors of 3969 are 1, 3, 7, 9, 21, 27, 49, 63, 81, 147, 189, 441, 567, 1323, and 3969

#### How to find factors of a number

 1.   Find factors of 3969 using Division Method 2.   Find factors of 3969 using Prime Factorization 3.   Find factors of 3969 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 3969

• Divide 3969 by 1: 3969 ÷ 1 : Remainder = 0
• Divide 3969 by 3: 3969 ÷ 3 : Remainder = 0
• Divide 3969 by 7: 3969 ÷ 7 : Remainder = 0
• Divide 3969 by 9: 3969 ÷ 9 : Remainder = 0
• Divide 3969 by 21: 3969 ÷ 21 : Remainder = 0
• Divide 3969 by 27: 3969 ÷ 27 : Remainder = 0
• Divide 3969 by 49: 3969 ÷ 49 : Remainder = 0
• Divide 3969 by 63: 3969 ÷ 63 : Remainder = 0
• Divide 3969 by 81: 3969 ÷ 81 : Remainder = 0
• Divide 3969 by 147: 3969 ÷ 147 : Remainder = 0
• Divide 3969 by 189: 3969 ÷ 189 : Remainder = 0
• Divide 3969 by 441: 3969 ÷ 441 : Remainder = 0
• Divide 3969 by 567: 3969 ÷ 567 : Remainder = 0
• Divide 3969 by 1323: 3969 ÷ 1323 : Remainder = 0
• Divide 3969 by 3969: 3969 ÷ 3969 : Remainder = 0

Hence, Factors of 3969 are 1, 3, 7, 9, 21, 27, 49, 63, 81, 147, 189, 441, 567, 1323, and 3969

#### 2. Steps to find factors of 3969 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 3969 using the division method, follow these steps:

• Step 1. Start dividing 3969 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 3969, which is 3. Divide 3969 by 3 to obtain the quotient (1323).
3969 ÷ 3 = 1323
• Step 3. Repeat step 1 with the obtained quotient (1323).
1323 ÷ 3 = 441
441 ÷ 3 = 147
147 ÷ 3 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1

So, the prime factorization of 3969 is, 3969 = 3 x 3 x 3 x 3 x 7 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 3969 as shown below:

So, the prime factorization of 3969 is, 3969 = 3 x 3 x 3 x 3 x 7 x 7.

#### 3. Find factors of 3969 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 3969 would be the two numbers which, when multiplied, give 3969 as the result.

The following table represents the calculation of factors of 3969 in pairs:

Factor Pair Pair Factorization
1 and 3969 1 x 3969 = 3969
3 and 1323 3 x 1323 = 3969
7 and 567 7 x 567 = 3969
9 and 441 9 x 441 = 3969
21 and 189 21 x 189 = 3969
27 and 147 27 x 147 = 3969
49 and 81 49 x 81 = 3969
63 and 63 63 x 63 = 3969

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 3969. They are called negative pair factors.

Hence, the negative pairs of 3969 would be ( -1 , -3969 ) , ( -3 , -1323 ) , ( -7 , -567 ) , ( -9 , -441 ) , ( -21 , -189 ) , ( -27 , -147 ) , ( -49 , -81 ) and ( -63 , -63 ) .

#### How can we define factors?

In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.

#### Properties of factors

• Every factor of a number is an exact divisor of that number, example 1, 3, 7, 9, 21, 27, 49, 63, 81, 147, 189, 441, 567, 1323, 3969 are exact divisors of 3969.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 3969 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 3969.

• Which is the smallest prime factor of 3969?

Smallest prime factor of 3969 is 3.

• Is 3969 a perfect square?

Yes 3969 is a perfect square.

• What are five multiples of 3969?

First five multiples of 3969 are 7938, 11907, 15876, 19845, 23814.

• What is prime factorization of 3969?

Prime factorization of 3969 is 3 x 3 x 3 x 3 x 7 x 7.

• What are factors of 3969?

Factors of 3969 are 1, 3, 7, 9, 21, 27, 49, 63, 81, 147, 189, 441, 567, 1323, 3969.

• How do you find factors of a negative number? ( eg. -3969 )?

Factors of -3969 are -1, -3, -7, -9, -21, -27, -49, -63, -81, -147, -189, -441, -567, -1323, -3969.

• Is 3969 a whole number?

Yes 3969 is a whole number.

• Which is greatest factor of 3969?

The greatest factor of 3969 is 1323.

• What are the prime factors of 3969?

The factors of 3969 are 1, 3, 7, 9, 21, 27, 49, 63, 81, 147, 189, 441, 567, 1323, 3969.
Prime factors of 3969 are 3, 3, 3, 3, 7, 7.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 3969. Can you help her?

Prime factors of 3969 are 3, 3, 3, 3, 7, 7.
Hence, the product of prime factors of 21.

Can you help Rubel to find out the product of the even factors of 3969?

Factors of 3969 are 1, 3, 7, 9, 21, 27, 49, 63, 81, 147, 189, 441, 567, 1323, 3969.
Even factors of 3969 are 0.
Hence, product of even factors of 3969 is; 0 = 0.

Joy wants to calculate mean of all the factors of 3969. Help him in finding the mean of 3969.

Factors of 3969 are 1, 3, 7, 9, 21, 27, 49, 63, 81, 147, 189, 441, 567, 1323, 3969.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 3969 is 1 + 3 + 7 + 9 + 21 + 27 + 49 + 63 + 81 + 147 + 189 + 441 + 567 + 1323 + 3969 = 6897.
Hence, the mean of factors of 3969 is 6897 ÷ 15 = 459.80.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 3969? Help her in writing all the factors.

Positive factors are 1, 3, 7, 9, 21, 27, 49, 63, 81, 147, 189, 441, 567, 1323, 3969.
Negative factors are -1, -3, -7, -9, -21, -27, -49, -63, -81, -147, -189, -441, -567, -1323, -3969.

How many factors are there for 3969?

Factors of 3969 are 1, 3, 7, 9, 21, 27, 49, 63, 81, 147, 189, 441, 567, 1323, 3969.
So there are in total 15 factors.

Joey wants to write all the prime factors of 3969 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 3969 are 3, 3, 3, 3, 7, 7.
So in exponential form it can be written as 34 x 72.

Kevin has been asked to write 14 factor(s) of 3969. Can you predict the answer?

14 factor(s) of 3969 are 1, 3, 7, 9, 21, 27, 49, 63, 81, 147, 189, 441, 567, 1323.