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Factors of 354: Prime Factorization, Methods, and Examples

There is a total of 8 factors of 354, meaning when 354 is divided by any of these integers, the answer is not a fraction or decimal number but an integer.

 It is understood that an even number such as 354 can never be a prime number, as along with 1 and 354, 2 is also a factor because 2 is a factor of all the even numbers.

Factors of 354

Here are the factors of number 354.

Factors of 354: 1, 2, 3, 6, 59, 118, 177 and 354

Negative Factors of 354

The negative factors of 354 are similar to their positive aspects, just with a negative sign.

Negative Factors of 354: -1, -2, -3, -6, -59, -118, -177 and -354

Prime Factorization of 354

The prime factorization of 354 is the way of expressing its prime factors in the product form.

Prime Factorization: 2 x 3 x 59

In this article, we will learn about the factors of 354 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 354?

The factors of 354 are 1, 2, 3, 6, 59, 118, 177, and 354. These numbers are the factors as they do not leave any remainder when divided by 354.

The factors of 354 are classified as prime numbers and composite numbers. The prime factors of the number 354 can be determined using the prime factorization technique.

How To Find the Factors of 354?

You can find the factors of 354 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 354, create a list containing the numbers that are exactly divisible by 354 with zero remainders. One important thing to note is that 1 and 354 are the 354’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 354 are determined as follows:

\[\dfrac{354}{1} = 354\]

\[\dfrac{354}{2} = 177\]

\[\dfrac{354}{3} = 118\]

\[\dfrac{354}{6} = 59\]

\[\dfrac{354}{354} = 1\]

Therefore, 1, 2, 3, 6, 59, 118, 177, and 354 are the factors of 354.

Total Number of Factors of 354

For 354, there are eight positive factors and eight negative ones. So in total, there are 16 factors of 354. 

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 354 is given as:

Factorization of 354 is 1 x 2 x 3 x 59.

The exponent of 2, 3, and 59 is 1.

Adding 1 to each and multiplying them together results in 16.

Therefore, the total number of factors of 354 is 16. 8 are positive, and eight 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 354 by Prime Factorization

The number 354 is composite. 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 354 using prime factorization, let us see 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 354, divide 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 354 can be expressed as:

354 = 2 x 3 x 59

Factors of 354 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.

For 354, the factor pairs can be found as:

1 x 354 = 354

2 x 177 = 354 

3 x 118 = 354 

6 x 59 = 354 

The possible factor pairs of 354 are given as (1, 354), (2, 177), (3, 118), and (6, 59 ).

All these numbers in pairs, when multiplied, give 354 as the product.

The negative factor pairs of 354 are given as:

-1 x -354 = 354

-2 x -177 = 354 

-3 x -118 = 354 

-6 x -59 = 354 

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, -2, -3, -6, -59, -118, -177 and -354 are called negative factors of 354.

The list of all the factors of 354, including positive and negative numbers, is given below.

Factor list of 354: 1, -1, 2, -2, 3, -3, 6, -6, 59, -59, 118, -118,  177, -177, 354 and -354.

Factors of 354 Solved Examples

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

Example 1

How many factors of 354 are there?

Solution

The total number of Factors of 354 is 8.

Factors of 354 are 1, 2, 3, 6, 59, 118, 177 and 354

Example 2

Find the factors of 354 using prime factorization.

Solution

The prime factorization of 354 is given as:

354 $\div$ 2 = 177 

177 $\div$ 3 =59 

59 $\div$ 59 = 1 

So the prime factorization of 354 can be written as:

2 x 3 x 59 = 354

Factors of 353|Factors List| Factors of 355

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