Factors of 455

The factors of 455 are the numbers that divide 455 evenly.

Positive Factors: These are the positive numbers that divide 455 evenly.

Positive factors are 1, 5, 7, 13, 35, 65, 91, and 455.

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

Negative factors are -1, -5, -7, -13, -35, -65, -91, -455

Prime Factors: Prime factors are the prime numbers themselves, when multiplied together, give 455 as the product.

Prime factors: 5, 7, 13

Prime Factorization: Prime factorization involves breaking 455 into its prime factors.

It is expressed as 5 × 7 × 13
 

Table listing the factors of 455

This breakdown helps in understanding the various factors of 455, whether they are positive or negative, as well as how prime factorization works for this number.

Finding the factors of a number consists of various methods, such as:

Methods to find the factors of 455:

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 455 as their product.

Step 1: Find the pair of numbers whose product is 455.

Step 2: The factors are those numbers, when multiplied, give 455.

Step 3: Make a list of numbers whose product will be 455.

A list of numbers whose products are 455 is given below:

• 1 × 455 = 455
• 5 × 91 = 455
• 7 × 65 = 455
• 13 × 35 = 455

Thus, the factors of 455 are 1, 5, 7, 13, 35, 65, 91, and 455.
 

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: 455 ÷ 1 = 455

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 455 are 1, 5, 7, 13, 35, 65, 91, and 455

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 455: Number 455 has only three prime factors.

Prime factors of 455: 5, 7, 13

To find the prime factors of 455, we can divide 455 with the prime numbers like 5, 7, and 13 from the list of factors of 455.

Step 1: Divide 455 with the prime number 5. 455 ÷ 5 = 91

Step 2: Divide 91 with the prime number 7. 91 ÷ 7 = 13

Step 3: Divide 13 with the prime number 13. 13 ÷ 13 = 1

Prime Factorization of 455: Prime Factorization breaks down the prime factors of 455.
Expressed as 5¹ × 7¹ × 13¹

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 455 into its prime factors: 5 × 7 × 13

Positive and Negative Factor Pairs of 455

Factors of 455 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, 455), (5, 91), (7, 65), (13, 35)

Negative Factor Pairs: (-1, -455), (-5, -91), (-7, -65), (-13, -35)

• Factors: Numbers that can divide a given number completely without leaving a remainder.

• Prime Factors: Prime numbers that, when multiplied together, yield the given number as their product.

• Prime Factorization: The process of breaking down a number into its prime factors and expressing it as a product of prime numbers.

• Multiple: Numbers are obtained when another number is multiplied by an integer.

• Perfect Square: When a number is multiplied twice, the resulting product will be an integer and will not have any decimal units.