# Factors of 345

Factors of 345 are 1, 3, 5, 15, 23, 69, 115, and 345

#### How to find factors of a number

 1.   Find factors of 345 using Division Method 2.   Find factors of 345 using Prime Factorization 3.   Find factors of 345 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 345

• Divide 345 by 1: 345 ÷ 1 : Remainder = 0
• Divide 345 by 3: 345 ÷ 3 : Remainder = 0
• Divide 345 by 5: 345 ÷ 5 : Remainder = 0
• Divide 345 by 15: 345 ÷ 15 : Remainder = 0
• Divide 345 by 23: 345 ÷ 23 : Remainder = 0
• Divide 345 by 69: 345 ÷ 69 : Remainder = 0
• Divide 345 by 115: 345 ÷ 115 : Remainder = 0
• Divide 345 by 345: 345 ÷ 345 : Remainder = 0

Hence, Factors of 345 are 1, 3, 5, 15, 23, 69, 115, and 345

#### 2. Steps to find factors of 345 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 345 using the division method, follow these steps:

• Step 1. Start dividing 345 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 345, which is 3. Divide 345 by 3 to obtain the quotient (115).
345 ÷ 3 = 115
• Step 3. Repeat step 1 with the obtained quotient (115).
115 ÷ 5 = 23
23 ÷ 23 = 1

So, the prime factorization of 345 is, 345 = 3 x 5 x 23.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 345 as shown below:

So, the prime factorization of 345 is, 345 = 3 x 5 x 23.

#### 3. Find factors of 345 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 345 would be the two numbers which, when multiplied, give 345 as the result.

The following table represents the calculation of factors of 345 in pairs:

Factor Pair Pair Factorization
1 and 345 1 x 345 = 345
3 and 115 3 x 115 = 345
5 and 69 5 x 69 = 345
15 and 23 15 x 23 = 345

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 345. They are called negative pair factors.

Hence, the negative pairs of 345 would be ( -1 , -345 ) , ( -3 , -115 ) , ( -5 , -69 ) and ( -15 , -23 ) .

#### 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, 15, 23, 69, 115, 345 are exact divisors of 345.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 345 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 345.

• What are the prime factors of 345?

The factors of 345 are 1, 3, 5, 15, 23, 69, 115, 345.
Prime factors of 345 are 3, 5, 23.

• What two numbers make 345?

Two numbers that make 345 are 3 and 115.

• What is the greatest prime factors of 345?

The greatest prime factor of 345 is 23.

• What are factors of 345?

Factors of 345 are 1, 3, 5, 15, 23, 69, 115, 345.

• How do you find factors of a negative number? ( eg. -345 )?

Factors of -345 are -1, -3, -5, -15, -23, -69, -115, -345.

• What are five multiples of 345?

First five multiples of 345 are 690, 1035, 1380, 1725, 2070.

• Write some multiples of 345?

First five multiples of 345 are 690, 1035, 1380, 1725.

• Is 345 a perfect square?

No 345 is not a perfect square.

• What two numbers make 345?

Two numbers that make 345 are 3 and 115.

#### Examples of Factors

What is prime factorization of 345?

Prime factorization of 345 is 3 x 5 x 23 = 3 x 5 x 23.

Sammy is puzzled while calculating the prime factors of 345. Can you help him find them?

Factors of 345 are 1, 3, 5, 15, 23, 69, 115, 345.
Prime factors of 345 are 3, 5, 23

Kevin has been asked to write 7 factor(s) of 345. Can you predict the answer?

7 factor(s) of 345 are 1, 3, 5, 15, 23, 69, 115.

Joey wants to write all the prime factors of 345 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 345 are 3, 5, 23.
So in exponential form it can be written as 3 x 5 x 23.

How many factors are there for 345?

Factors of 345 are 1, 3, 5, 15, 23, 69, 115, 345.
So there are in total 8 factors.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 345? Help her in writing all the factors.

Positive factors are 1, 3, 5, 15, 23, 69, 115, 345.
Negative factors are -1, -3, -5, -15, -23, -69, -115, -345.

Can you help Rubel to find out the product of the even factors of 345?

Factors of 345 are 1, 3, 5, 15, 23, 69, 115, 345.
Even factors of 345 are 0.
Hence, product of even factors of 345 is; 0 = 0.