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Factors of 467: Prime Factorization, Methods, and Examples

The factors of 467 are the listings of the numbers that can be perfectly divided by 467 without any remainder. The number 467 is a prime number which is why it is divisibly by 1 and itself only. 

Let us find out more about its factors.

Factors of 467

Here are the factors of number 467.

Factors of 467: 1 and 467

Negative Factors of 467

The negative factors of 467 are similar to their positive aspects, just with a negative sign.

Negative Factors of 467: -1 and -467

Prime Factorization of 467

The prime factorization of 467 is the way of expressing its prime factors in the product form.

Prime Factorization: 1 x 467

In this article, we will learn about the factors of 467 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 467?

The factors of 467 are 1 and 467. These numbers are the factors as they do not leave any remainder when divided by 467.

The factors of 467 are classified as prime numbers and composite numbers. The prime factors of the 467 can be determined using the prime factorization technique.

How To Find the Factors of 467?

You can find the factors of 467 by using the rules of divisibility. The divisibility rule states that any number, when divided by any other natural number, is said to be divisible by the number if the quotient is the whole number and the resulting remainder is zero.

To find the factors of 467, create a list containing the numbers precisely divisible by 467 with zero remainders. One important thing to note is that 1 and 467 are 467’s factors, as every natural number has 1 and the number itself as its factor.

1 is also called the universal factor of every number. The factors of 467 are determined as follows:

\[\dfrac{467}{1} = 467\]

Therefore, 1 and 467 are the factors of 467.

Total Number of Factors of 467

For 467, there are two positive factors and two negative ones. So in total, there are four factors of 467. 

To find the total number of factors of the given number, follow the procedure mentioned below:

  1. Find the factorization/prime factorization of the given number.
  2. Demonstrate the prime factorization of the number in the exponent form.
  3. Add 1 to each of the exponents of the prime factor.
  4. Now, multiply the resulting exponents together. This obtained product is equivalent to the total number of factors of the given number.

By following this procedure, the total number of factors of X is given as:

Factorization of 467 is 1 x 467.

The exponent of 1 and 467 is 1.

Adding 1 to each and multiplying them together results in four.

Therefore, the total number of factors of 467 is four. Two positive and two factors are negative.

Important Notes

Here are some essential points that must be considered while finding the factors of any given number:

  • The factor of any given number must be a whole number.
  • The number factors cannot be in the form of decimals or fractions.
  • Factors can be positive as well as negative.
  • Negative factors are the additive inverse of the positive factors of a given number.
  • The factor of a number cannot be greater than that number.
  • Every even number has 2 as its prime factor, the smallest prime factor.

Factors of 467 by Prime Factorization

The number 467 is a prime number. Prime factorization is a valuable technique for finding the number’s prime factors and expressing the number as the product of its prime factors.

Before finding the factors of 467 using prime factorization, let us find out what prime factors are. Prime factors are the factors of any given number that are only divisible by 1 and themselves.

To start the prime factorization of 467, start dividing by its most minor prime factor. First, determine that the given number is either even or odd. If it is an even number, then 2 will be the smallest prime factor.

Continue splitting the quotient obtained until 1 is received as the quotient. The prime factorization of 467 can be expressed as:

467 = 1 x 467

Factors of 467 in Pairs

The factor pairs are the duplet of numbers that, when multiplied together, result in the factorized number. Factor pairs can be more than one depending on the total number of factors given.

For 467, the factor pairs can be found as:

1 x 467 = 467

The possible factor pairs of 467 are given as (1, 467).

All these numbers in pairs, when multiplied, give 467 as the product.

The negative factor pairs of 467 are given as:

-1 x -467 = 467 

It is important to note that in negative factor pairs, the minus sign has been multiplied by the minus sign, due to which the resulting product is the original positive number. Therefore, -1 and -467 are called negative factors of 467.

The list of all the factors of 467, including positive and negative numbers, is given below.

Factor list of 467: 1, -1, 467, and -467

Factors of 467 Solved Examples

To better understand the concept of factors, let’s solve some examples.

Example 1

How many factors of 467 are there?

Solution

The total number of Factors of 467 is m.

Factors of 467 are 1 and 467.

Example 2

Find the sum of factors of 467.

Solution

The sum of factors is given as:

Sum = 1 + 467 

Sum = 468

Factors of 466|Factors List| Factors of 468

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