# Factors of 441

Factors of 441 are 1, 3, 7, 9, 21, 49, 63, 147, and 441

#### How to find factors of a number

 1.   Find factors of 441 using Division Method 2.   Find factors of 441 using Prime Factorization 3.   Find factors of 441 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 441

• Divide 441 by 1: 441 ÷ 1 : Remainder = 0
• Divide 441 by 3: 441 ÷ 3 : Remainder = 0
• Divide 441 by 7: 441 ÷ 7 : Remainder = 0
• Divide 441 by 9: 441 ÷ 9 : Remainder = 0
• Divide 441 by 21: 441 ÷ 21 : Remainder = 0
• Divide 441 by 49: 441 ÷ 49 : Remainder = 0
• Divide 441 by 63: 441 ÷ 63 : Remainder = 0
• Divide 441 by 147: 441 ÷ 147 : Remainder = 0
• Divide 441 by 441: 441 ÷ 441 : Remainder = 0

Hence, Factors of 441 are 1, 3, 7, 9, 21, 49, 63, 147, and 441

#### 2. Steps to find factors of 441 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 441 using the division method, follow these steps:

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

So, the prime factorization of 441 is, 441 = 3 x 3 x 7 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 441 as shown below:

So, the prime factorization of 441 is, 441 = 3 x 3 x 7 x 7.

#### 3. Find factors of 441 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 441 would be the two numbers which, when multiplied, give 441 as the result.

The following table represents the calculation of factors of 441 in pairs:

Factor Pair Pair Factorization
1 and 441 1 x 441 = 441
3 and 147 3 x 147 = 441
7 and 63 7 x 63 = 441
9 and 49 9 x 49 = 441
21 and 21 21 x 21 = 441

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 441. They are called negative pair factors.

Hence, the negative pairs of 441 would be ( -1 , -441 ) , ( -3 , -147 ) , ( -7 , -63 ) , ( -9 , -49 ) and ( -21 , -21 ) .

#### How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

#### Properties of factors

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

• Which is the smallest prime factor of 441?

Smallest prime factor of 441 is 3.

• Is 441 a perfect square?

Yes 441 is a perfect square.

• What are five multiples of 441?

First five multiples of 441 are 882, 1323, 1764, 2205, 2646.

• What is prime factorization of 441?

Prime factorization of 441 is 3 x 3 x 7 x 7.

• What are factors of 441?

Factors of 441 are 1, 3, 7, 9, 21, 49, 63, 147, 441.

• How do you find factors of a negative number? ( eg. -441 )?

Factors of -441 are -1, -3, -7, -9, -21, -49, -63, -147, -441.

• Is 441 a whole number?

Yes 441 is a whole number.

• Which is greatest factor of 441?

The greatest factor of 441 is 147.

• What are the prime factors of 441?

The factors of 441 are 1, 3, 7, 9, 21, 49, 63, 147, 441.
Prime factors of 441 are 3, 3, 7, 7.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 441. Can you help her?

Prime factors of 441 are 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 441?

Factors of 441 are 1, 3, 7, 9, 21, 49, 63, 147, 441.
Even factors of 441 are 0.
Hence, product of even factors of 441 is; 0 = 0.

Joy wants to calculate mean of all the factors of 441. Help him in finding the mean of 441.

Factors of 441 are 1, 3, 7, 9, 21, 49, 63, 147, 441.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 441 is 1 + 3 + 7 + 9 + 21 + 49 + 63 + 147 + 441 = 741.
Hence, the mean of factors of 441 is 741 ÷ 9 = 82.33.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 441? Help her in writing all the factors.

Positive factors are 1, 3, 7, 9, 21, 49, 63, 147, 441.
Negative factors are -1, -3, -7, -9, -21, -49, -63, -147, -441.

How many factors are there for 441?

Factors of 441 are 1, 3, 7, 9, 21, 49, 63, 147, 441.
So there are in total 9 factors.

Joey wants to write all the prime factors of 441 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 441 are 3, 3, 7, 7.
So in exponential form it can be written as 32 x 72.

Kevin has been asked to write 8 factor(s) of 441. Can you predict the answer?

8 factor(s) of 441 are 1, 3, 7, 9, 21, 49, 63, 147.