# Factors of 1845

Factors of 1845 are 1, 3, 5, 9, 15, 41, 45, 123, 205, 369, 615, and 1845

#### How to find factors of a number

 1.   Find factors of 1845 using Division Method 2.   Find factors of 1845 using Prime Factorization 3.   Find factors of 1845 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 1845

• Divide 1845 by 1: 1845 ÷ 1 : Remainder = 0
• Divide 1845 by 3: 1845 ÷ 3 : Remainder = 0
• Divide 1845 by 5: 1845 ÷ 5 : Remainder = 0
• Divide 1845 by 9: 1845 ÷ 9 : Remainder = 0
• Divide 1845 by 15: 1845 ÷ 15 : Remainder = 0
• Divide 1845 by 41: 1845 ÷ 41 : Remainder = 0
• Divide 1845 by 45: 1845 ÷ 45 : Remainder = 0
• Divide 1845 by 123: 1845 ÷ 123 : Remainder = 0
• Divide 1845 by 205: 1845 ÷ 205 : Remainder = 0
• Divide 1845 by 369: 1845 ÷ 369 : Remainder = 0
• Divide 1845 by 615: 1845 ÷ 615 : Remainder = 0
• Divide 1845 by 1845: 1845 ÷ 1845 : Remainder = 0

Hence, Factors of 1845 are 1, 3, 5, 9, 15, 41, 45, 123, 205, 369, 615, and 1845

#### 2. Steps to find factors of 1845 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 1845 using the division method, follow these steps:

• Step 1. Start dividing 1845 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 1845, which is 3. Divide 1845 by 3 to obtain the quotient (615).
1845 ÷ 3 = 615
• Step 3. Repeat step 1 with the obtained quotient (615).
615 ÷ 3 = 205
205 ÷ 5 = 41
41 ÷ 41 = 1

So, the prime factorization of 1845 is, 1845 = 3 x 3 x 5 x 41.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1845 as shown below:

So, the prime factorization of 1845 is, 1845 = 3 x 3 x 5 x 41.

#### 3. Find factors of 1845 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 1845 would be the two numbers which, when multiplied, give 1845 as the result.

The following table represents the calculation of factors of 1845 in pairs:

Factor Pair Pair Factorization
1 and 1845 1 x 1845 = 1845
3 and 615 3 x 615 = 1845
5 and 369 5 x 369 = 1845
9 and 205 9 x 205 = 1845
15 and 123 15 x 123 = 1845
41 and 45 41 x 45 = 1845

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 1845. They are called negative pair factors.

Hence, the negative pairs of 1845 would be ( -1 , -1845 ) , ( -3 , -615 ) , ( -5 , -369 ) , ( -9 , -205 ) , ( -15 , -123 ) and ( -41 , -45 ) .

#### What are factors?

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

#### Properties of factors

• Every factor of a number is an exact divisor of that number, example 1, 3, 5, 9, 15, 41, 45, 123, 205, 369, 615, 1845 are exact divisors of 1845.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 1845 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 1845.

• Which is the smallest prime factor of 1845?

Smallest prime factor of 1845 is 3.

• Is 1845 a perfect square?

No 1845 is not a perfect square.

• What are five multiples of 1845?

First five multiples of 1845 are 3690, 5535, 7380, 9225, 11070.

• What is prime factorization of 1845?

Prime factorization of 1845 is 3 x 3 x 5 x 41.

• What are factors of 1845?

Factors of 1845 are 1, 3, 5, 9, 15, 41, 45, 123, 205, 369, 615, 1845.

• How do you find factors of a negative number? ( eg. -1845 )?

Factors of -1845 are -1, -3, -5, -9, -15, -41, -45, -123, -205, -369, -615, -1845.

• Is 1845 a whole number?

Yes 1845 is a whole number.

• Which is greatest factor of 1845?

The greatest factor of 1845 is 615.

• What are the prime factors of 1845?

The factors of 1845 are 1, 3, 5, 9, 15, 41, 45, 123, 205, 369, 615, 1845.
Prime factors of 1845 are 3, 3, 5, 41.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 1845. Can you help her?

Prime factors of 1845 are 3, 3, 5, 41.
Hence, the product of prime factors of 615.

Can you help Rubel to find out the product of the even factors of 1845?

Factors of 1845 are 1, 3, 5, 9, 15, 41, 45, 123, 205, 369, 615, 1845.
Even factors of 1845 are 0.
Hence, product of even factors of 1845 is; 0 = 0.

Joy wants to calculate mean of all the factors of 1845. Help him in finding the mean of 1845.

Factors of 1845 are 1, 3, 5, 9, 15, 41, 45, 123, 205, 369, 615, 1845.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 1845 is 1 + 3 + 5 + 9 + 15 + 41 + 45 + 123 + 205 + 369 + 615 + 1845 = 3276.
Hence, the mean of factors of 1845 is 3276 ÷ 12 = 273.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 1845? Help her in writing all the factors.

Positive factors are 1, 3, 5, 9, 15, 41, 45, 123, 205, 369, 615, 1845.
Negative factors are -1, -3, -5, -9, -15, -41, -45, -123, -205, -369, -615, -1845.

How many factors are there for 1845?

Factors of 1845 are 1, 3, 5, 9, 15, 41, 45, 123, 205, 369, 615, 1845.
So there are in total 12 factors.

Joey wants to write all the prime factors of 1845 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1845 are 3, 3, 5, 41.
So in exponential form it can be written as 32 x 5 x 41.

Kevin has been asked to write 11 factor(s) of 1845. Can you predict the answer?

11 factor(s) of 1845 are 1, 3, 5, 9, 15, 41, 45, 123, 205, 369, 615.