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Factors of 372: Prime Factorization, Methods, and Examples

The factors of 372 are the integers that divide the number evenly without a remainder. The number 372 is an even number. It is a composite number. 

In this article, we will discuss in this article how to find the factors of 371.

Factors of 372

Here are the factors of number 371.

Factors of 371: 1, 2, 3, 4, 6, 12, 31, 62, 93, 124, 186, and 372 

Negative Factors of 372

The negative factors of 372 are similar to their positive aspects, just with a negative sign.

Negative Factors of 372: –1, -2, -3, -4, -6, -12, -31, -62, -93, -124, -186, and -372 

Prime Factorization of 372

The prime factorization of 372 is the way of expressing its prime factors in the product form.

Prime Factorization: 2 x 2 x 3 x 31

In this article, we will learn about the factors of 372 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 372?

The factors of 372 are 1, 2, 3, 4, 6, 12, 31, 62, 93, 124, 186, and 372. These numbers are the factors as they do not leave any remainder when divided by 372.

The factors of 372 are classified as prime numbers and composite numbers. The prime factors of the number 372 can be determined using the prime factorization technique.

How To Find the Factors of 372?

You can find the factors of 372 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 372, create a list containing the numbers that are exactly divisible by 372 with zero remainders. One important thing to note is that 1 and 372 are the 372’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 372 are determined as follows:

\[\dfrac{372}{1} = 372\]

\[\dfrac{372}{2} = 186\]

\[\dfrac{372}{3} = 124\]

\[\dfrac{372}{4} = 93\]

\[\dfrac{372}{6} = 62\]

\[\dfrac{372}{12} = 31\]

Therefore, 1, 2, 3, 4, 6, 12, 31, 62, 93, 124, 186, and 372 are the factors of 372.

Total Number of Factors of 372

For 372, there are twelve positive factors and twelve negative ones. So in total, there are twenty-four factors of 372. 

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 form of 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 373 is given as:

Factorization of 373 is 1 x 2$^2^ x 3 x 31.

The exponent of 1, 3, and 31 is 1.

Adding 1 to each and multiplying them together results in 24.

Therefore, the total number of factors of 372 is 24. Twelve are positive, and twelve 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 factors of the number 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 372 by Prime Factorization

The number 372 is a 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 372 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 372, 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 372 can be expressed as:

372 = 2 x 2 x 3 x 31

Factors of 372 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 371, the factor pairs can be found as:

1 x 371 = 372

2 x 186 = 372 

3 x 124 = 372

4 x 93 = 372

6 x 62 = 372 

12 x 31 = 372   

The possible factor pairs of 372 are given as (1, 372), (2, 186), (3, 124),(4, 93), (6, 62), and (12, 31).

All these numbers in pairs, when multiplied, give 372 as the product.

The negative factor pairs of 372 are given as:

-1 x -371 = 372

-2 x -186 = 372 

-3 x -124 = 372

-4 x -93 = 372

-6 x -62 = 372 

-12 x -31 = 372 

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, -4, -6, -12, -31, -62, -93, -124, -186, and -372  are called negative factors of 372.

Factors of 372 Solved Examples

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

Example 1

How many factors of 372 are there?

Solution

The total number of Factors of 372 is 12.

Factors of 372 are 1, 2, 3, 4, 6, 12, 31, 62, 93, 124, 186, and 372.

Example 2

Find the factors of 372 using prime factorization.

Solution

The prime factorization of 372 is given as:

372 $\div$ 2 = 186

186 $\div$ 2 = 93

93 $\div$ 3 = 31 

31 $\div$ 31 = 1 

So the prime factorization of 372 can be written as:

2 x 2 x 3 x 31 = 372

Factors of 371|Factors List| Factors of 373

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