# Factors of 765

Factors of 765 are 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, and 765

#### How to find factors of a number

 1.   Find factors of 765 using Division Method 2.   Find factors of 765 using Prime Factorization 3.   Find factors of 765 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 765

• Divide 765 by 1: 765 ÷ 1 : Remainder = 0
• Divide 765 by 3: 765 ÷ 3 : Remainder = 0
• Divide 765 by 5: 765 ÷ 5 : Remainder = 0
• Divide 765 by 9: 765 ÷ 9 : Remainder = 0
• Divide 765 by 15: 765 ÷ 15 : Remainder = 0
• Divide 765 by 17: 765 ÷ 17 : Remainder = 0
• Divide 765 by 45: 765 ÷ 45 : Remainder = 0
• Divide 765 by 51: 765 ÷ 51 : Remainder = 0
• Divide 765 by 85: 765 ÷ 85 : Remainder = 0
• Divide 765 by 153: 765 ÷ 153 : Remainder = 0
• Divide 765 by 255: 765 ÷ 255 : Remainder = 0
• Divide 765 by 765: 765 ÷ 765 : Remainder = 0

Hence, Factors of 765 are 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, and 765

#### 2. Steps to find factors of 765 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 765 using the division method, follow these steps:

• Step 1. Start dividing 765 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 765, which is 3. Divide 765 by 3 to obtain the quotient (255).
765 ÷ 3 = 255
• Step 3. Repeat step 1 with the obtained quotient (255).
255 ÷ 3 = 85
85 ÷ 5 = 17
17 ÷ 17 = 1

So, the prime factorization of 765 is, 765 = 3 x 3 x 5 x 17.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 765 as shown below:

So, the prime factorization of 765 is, 765 = 3 x 3 x 5 x 17.

#### 3. Find factors of 765 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 765 would be the two numbers which, when multiplied, give 765 as the result.

The following table represents the calculation of factors of 765 in pairs:

Factor Pair Pair Factorization
1 and 765 1 x 765 = 765
3 and 255 3 x 255 = 765
5 and 153 5 x 153 = 765
9 and 85 9 x 85 = 765
15 and 51 15 x 51 = 765
17 and 45 17 x 45 = 765

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 765. They are called negative pair factors.

Hence, the negative pairs of 765 would be ( -1 , -765 ) , ( -3 , -255 ) , ( -5 , -153 ) , ( -9 , -85 ) , ( -15 , -51 ) and ( -17 , -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, 17, 45, 51, 85, 153, 255, 765 are exact divisors of 765.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 765 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 765.

• Which is the smallest prime factor of 765?

Smallest prime factor of 765 is 3.

• Is 765 a perfect square?

No 765 is not a perfect square.

• What are five multiples of 765?

First five multiples of 765 are 1530, 2295, 3060, 3825, 4590.

• What is prime factorization of 765?

Prime factorization of 765 is 3 x 3 x 5 x 17.

• What are factors of 765?

Factors of 765 are 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 765.

• How do you find factors of a negative number? ( eg. -765 )?

Factors of -765 are -1, -3, -5, -9, -15, -17, -45, -51, -85, -153, -255, -765.

• Is 765 a whole number?

Yes 765 is a whole number.

• Which is greatest factor of 765?

The greatest factor of 765 is 255.

• What are the prime factors of 765?

The factors of 765 are 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 765.
Prime factors of 765 are 3, 3, 5, 17.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 765. Can you help her?

Prime factors of 765 are 3, 3, 5, 17.
Hence, the product of prime factors of 255.

Can you help Rubel to find out the product of the even factors of 765?

Factors of 765 are 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 765.
Even factors of 765 are 0.
Hence, product of even factors of 765 is; 0 = 0.

Joy wants to calculate mean of all the factors of 765. Help him in finding the mean of 765.

Factors of 765 are 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 765.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 765 is 1 + 3 + 5 + 9 + 15 + 17 + 45 + 51 + 85 + 153 + 255 + 765 = 1404.
Hence, the mean of factors of 765 is 1404 ÷ 12 = 117.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 765? Help her in writing all the factors.

Positive factors are 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 765.
Negative factors are -1, -3, -5, -9, -15, -17, -45, -51, -85, -153, -255, -765.

How many factors are there for 765?

Factors of 765 are 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 765.
So there are in total 12 factors.

Joey wants to write all the prime factors of 765 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 765 are 3, 3, 5, 17.
So in exponential form it can be written as 32 x 5 x 17.

Kevin has been asked to write 11 factor(s) of 765. Can you predict the answer?

11 factor(s) of 765 are 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255.