Factors of 345

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

Positive Factors: These are negative counterparts of the positive factors.

Positive factors: 1, 3, 5, 15, 23, 69, 115, 345

Negative Factors: These are the negative counterparts of the positive factors.

Negative factors: -1, -3, -5, -15, -23, -69, -115, -345

Prime Factors: Prime factors are the prime numbers that, when multiplied together, give 345 as the product.
Prime factors: 3, 5, 23

Prime Factorization: Prime factorization involves breaking 345 into its prime factors.
It is expressed as 3 × 5 × 23
 

There are different methods to find the factors of 345.

Methods to find the factors of 345:

• Multiplication Method
• Division Method
• Prime Factor and Prime Factorization
• Factor Tree

This breakdown helps in understanding the various factors of 345, whether they are positive or negative, and how prime factorization works for this number.
 

The multiplication method finds the pairs of factors that give 345 as their product.

Step 1: Find the pair of numbers whose product is 345.
Step 2: The factors are those numbers, which when multiplied, give 345.
Step 3: Make a list of numbers whose product will be 345.

A list of numbers whose products are 345 is given below:
1 × 345 = 345
3 × 115 = 345
5 × 69 = 345
15 × 23 = 345

Thus, the factors of 345 are 1, 3, 5, 15, 23, 69, 115, and 345.
 

The division method finds the numbers that fully divide the given number. The steps are given below:

Step 1: Since every number is divisible by 1, 1 will always be a factor. Example: 345 ÷ 1 = 345

Step 2: Move to the next integer. The factors of the number include the divisor and the quotient obtained after division.

Thus, the factors of 345 are 1, 3, 5, 15, 23, 69, 115, and 345
 

Multiplying prime numbers to get the given number as their product is called prime factors. A number when simplified using the factors of that number and expressed in the form of prime factors is the prime factorization of a number.

Prime Factors of 345: Number 345 has three prime factors.
Prime factors of 345: 3, 5, 23

To find the prime factors of 345, we can divide 345 by the prime numbers like 3, 5, and 23 from the list of factors of 345.

Step 1: Divide 345 by the prime number 3:
345 ÷ 3 = 115
Step 2: Divide 115 by the prime number 5:
115 ÷ 5 = 23
Step 3: Divide 23 by the prime number 23:
23 ÷ 23 = 1

Prime Factorization of 345:

Prime factorization breaks down the prime factors of 345.

Expressed as 3 × 5 × 23
 

The prime factorization is visually represented using the factor tree. It helps to understand the process easily.

This tree shows the breakdown of 345 into its prime factors: 3 × 5 × 23. Each branch splits into prime factors.

Factors of 345 can be written in both positive pairs and negative pairs. They are like team members. Their product will be equal to the number given.

Positive Factor Pairs: (1, 345), (3, 115), (5, 69), (15, 23)

Negative Factor Pairs: (-1, -345), (-3, -115), (-5, -69), (-15, -23)
 

• Factors: Numbers that can divide a given number completely without leaving a remainder. For example, the factors of 345 are 1, 3, 5, 15, 23, 69, 115, and 345.

• Prime Factors: Prime numbers that, when multiplied together, result in the original number. For 345, the prime factors are 3, 5, and 23.

• Prime Factorization: The process of expressing a number as the product of its prime factors. For 345, the prime factorization is 3 × 5 × 23.

• Multiple: A number that can be obtained by multiplying a given number by an integer. For example, 345 is a multiple of 5.

• Perfect Square: A number that results when an integer is multiplied by itself. In the factors of 345, the only perfect square is 1 (1 × 1).