Factors of 465

The factors of 465 are the numbers that divide 465 evenly.

Positive Factors: These are the positive numbers that divide 465 evenly.

Positive factors are 1, 3, 5, 7, 9, 15, 31, 45, 65, 93, 155, and 465.

Negative Factors: These are negative counterparts of the positive factors. Negative factors: -1, -3, -5, -7, -9, -15, -31, -45, -65, -93, -155, -465.

Prime Factors: Prime factors are the prime numbers themselves, when multiplied together, give 465 as the product. Prime factors: 3, 5, 31.

Prime Factorization: Prime factorization involves breaking 465 into its prime factors. It is expressed as 3 × 5 × 7.

Table listing the factors of 465

This breakdown helps in understanding the various factors of 465, whether they are positive or negative, as well as how prime factorization works for this number.

Finding the factors of 465, we can make use of various methods. The methods are listed below.

Methods to find the factors of 465:

1. Multiplication Method
2. Division Method
3. Prime Factor and Prime Factorization
4. Factor Tree

The multiplication method finds the pair of factors that give 465 as their product.

Step 1: Find the pair of numbers whose product is 465.

Step 2: The factors are those numbers, when multiplied, give 465.

Step 3: Make a list of numbers whose product will be 465.

A list of numbers whose products are 465 is given below:

• 1 × 465 = 465
• 3 × 155 = 465
• 5 × 93 = 465
• 7 × 65 = 465
• 9 × 45 = 465
• 15 × 31 = 465

Thus, the factors of 465 are 1, 3, 5, 7, 9, 15, 31, 45, 65, 93, 155, and 465.
 

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: 465 ÷ 1 = 465

Step 2: Move to the next integer. The factors of the number include the number that is used to divide and the number of times the particular number is divided.

Thus, the factors of 465 are 1, 3, 5, 7, 9, 15, 31, 45, 65, 93, 155, and 465.

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

Prime Factors of 465: Number 465 has three prime factors.

Prime factors of 465: 3, 5, 31

To find the prime factors of 465, we can divide 465 with the prime numbers like 3, 5, and 31 from the list of factors of 465.

Step 1: Divide 465 with the prime number 3

• 465 ÷ 3 = 155

Step 2: Divide 155 with the prime number 5

• 155 ÷ 5 = 31

Step 3: Divide 31 with the prime number 7

• 31 ÷ 31  = 1

Prime Factorization of 465: Prime Factorization breaks down the prime factors of 465.

Expressed as 3 × 5 × 31

The prime factorization is visually represented using the factor tree. It helps to understand the process easily. In this factor tree, each branch splits into prime factors.

This tree shows the breakdown of 465 into its prime factors: 3 × 5 × 31

Positive and Negative Factor Pairs of 465

Factors of 465 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, 465), (3, 155), (5, 93), (7, 65), (9, 45), (15, 31)

Negative Factor Pairs: (-1, -465), (-3, -155), (-5, -93), (-7, -65), (-9, -45), (-15, -31)

• Factors: Numbers that can divide a given number completely without leaving a remainder. Example: The factors of 379 are 1 and 379.

• Prime Factors: Prime numbers from the list of factors of a particular number, when multiplied together, give the original number. Since 379 is a prime number, its prime factors are just 379 itself.

• Prime Factorization: The process of breaking down a number into its prime factors. The prime factorization of 379 is simply 379.

• Multiple: A number that is the product of a given number and another integer. For example, multiples of 7 are 7, 14, 21, etc.

• Perfect Square: A number that is the product of an integer multiplied by itself. For example, 25 is a perfect square because 5 × 5 = 25.