Factors of 629: Prime Factorization, Methods, and Examples

The factors of 629 are the listings of integer that 629 evenly. The factors of a  number can also be paired in a group such that their product is equivalent to that particular number. The number 629 has four factors in total. 

Factors Of 629

Let us determine the factors of 629.

Factors of 629

Here are the factors of number 629.

Factors of 629: 1, 17, 37, and 629

Negative Factors of 629

The negative factors of 629 are similar to its positive aspects, just with a negative sign.

Negative Factors of 629: -1, -17, -37, and -629

Prime Factorization of 629

The prime factorization of 629 is the way of expressing its prime factors in the product form.

Prime Factorization: 17 x 37

In this article, we will learn about the factors of 629 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 629?

The factors of 629 are 1, 17, 37, and 629. These numbers are the factors as they do not leave any remainder when divided by 629.

The factors of 629 are classified as prime numbers and composite numbers. The prime factors of the number 629 can be determined using the prime factorization technique.

How To Find the Factors of 629?

You can find the factors of 629 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 629, create a list containing the numbers that are exactly divisible by 629 with zero remainders. One important thing to note is that 1 and 629 are 629’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 629 are determined as follows:

\[\dfrac{629}{1} = 629\]

\[\dfrac{629}{17} = 37\]

Therefore, 1, 17, 37, and 629 are the factors of 629.

Total Number of Factors of 629

For 629, there are four positive factors and four negative ones. So in total, there are eight factors of 629. 

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 629 is given as:

Factorization of 629 is 1 x 17 x 37.

The exponent of 1, 17, and 37 is 1.

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

Therefore, the total number of factors of 629 is eight. Four are positive, and four 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 629 by Prime Factorization

The number 629 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.prime factorization of 629

Before finding the factors of 629 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 629, 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 629 can be expressed as:

629 = 17 x 37

Factors of 629 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.Factors of 629 in Pairs

For 629, the factor pairs can be found as:

1 x 629 = 629

17 x 37 = 629 

The possible factor pairs of 629 are given as (1, 629) and (17, 37).

All these numbers in pairs, when multiplied, give 629 as the product.

The negative factor pairs of 629 are given as:

-1 x -629 = 629 

-17 x -37 = 629

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, -17, -37, and -629 are called negative factors of 629.

The list of all the factors of 629, including positive as well as negative numbers, is given below.

Factor list of 629: 1, -1, 17, -17, 37, -37, 629, and -629

Factors of 629 Solved Examples

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

Example 1

How many factors of 629 are there?


The total number of Factors of 629 is four.

Factors of 629 are 1, 17, 37, and 629.

Example 2

Find the factors of 629 using prime factorization.


The prime factorization of 629 is given as:

629 $\div$ 17 = 37 

37 $\div$ 37 = 1 

So the prime factorization of 629 can be written as:

17 x 37 = 629

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