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Factors of 637: Prime Factorization, Methods, and Examples

The factors of 637 are those factors that are completely divisible by 637 giving a whole number quotient and 0 remainders. 

It becomes a composite number because it has six factors that are evenly divisible by 637.

Factors of 637

Here are the factors of number 637.

Factors of 637:  1, 7, 13, 49, 91, and 637

Negative Factors of 637

The negative factors of 637 are similar to its positive aspects, just with a negative sign.

Negative Factors of 637: -1, -7, -13, -49, -91, and -637

Prime Factorization of 637

The prime factorization of 637 is the way of expressing its prime factors in the product form.

Prime Factorization: 7 x 7 x 13

In this article, we will learn about the factors of 637 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 637?

The factors of 637 are 1, 7, 13, 49, 91, and 637. These numbers are the factors as they do not leave any remainder when divided by 637.

The factors of 637 are classified as prime numbers and composite numbers. The prime factors of the number 637 can be determined using the prime factorization technique.

How To Find the Factors of 637?

You can find the factors of 637 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 637, create a list containing the numbers that are exactly divisible by 637 with zero remainders. One important thing to note is that 1 and 637 are the 637’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 637 are determined as follows:

\[\dfrac{637}{1} = 637\]

\[\dfrac{637}{7} = 91\]

\[\dfrac{637}{13} = 49\]

\[\dfrac{637}{49} = 13\]

\[\dfrac{637}{91} = 7\]

\[\dfrac{637}{637} = 1\]

Therefore, 1, 7, 13, 49, 91, and 637 are the factors of 637.

Total Number of Factors of 637

For 637, there are six positive factors and six negative ones. So in total, there are twelve factors of 637. 

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 637 is given as:

Factorization of 637 is 7 x 7 x 13.

The exponent of 7, 7,13 is 2 and 1 respectively.

Adding 1 to each and multiplying them together results in 6.

Therefore, the total number of factors of 637 is 12 whereas six are positive, and six 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 637 by Prime Factorization

The number 637 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 637 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 637, 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 637 can be expressed as:

637 = 7 x 7 x 13

Factors of 637 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 637, the factor pairs can be found as:

1 x 637 = 637

7 x 91 = 637

13 x 49 = 637

The possible factor pairs of 637 are given as (1, 637), (7, 91), and (13, 49).

All these numbers in pairs, when multiplied, give 637 as the product.

The negative factor pairs of 637 are given as:

-1 x -637 = 637

-7 x -91 = 637

-13 x -49 = 637

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, -7, -13, -49, -91, and -637 are called negative factors of 637.

The list of all the factors of 637, including positive as well as negative numbers, is given below.

Factor list of 637: 1, -1, 7, -7, 13, -13, 49, -49, 91, -91, 637, and -637

Factors of 637 Solved Examples

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

Example 1

How many factors of 637 are there?

Solution

The total number of Factors of 637 is six.

Factors of 637 are 1, 7, 13, 49, 91, and 637.

Example 2

Find the factors of 637 using prime factorization.

Solution

The prime factorization of 637 is given as:

637 $\div$ 7 = 91 

91 $\div$ 7 = 13 

13 $\div$ 13 = 1

So the prime factorization of 637 can be written as:

7 x 7 x 13 = 637

Factors of 636|Factors List| Factors of 638

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