 # Factors of 630: Prime Factorization, Methods, and Examples

The factors of 630 are numbers that divide 630 completely. There are 24 factors of 630 in total which means that it is a composite number. The given number’s factors can be positive and negative, provided that the given number is achieved upon multiplication of two-factor integers.

### Factors of 630

Here are the factors of number 630.

Factors of 630: 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, and 630

### Negative Factors of 630

The negative factors of 630 are similar to its positive aspects, just with a negative sign.

Negative Factors of 630: –1, -2, -3, -5, -6, -7, -9, -10, -14, -15, -18, -21, -30, -35, -42, -45, -63, -70, -90, -105, -126, -210, -315, and -630

### Prime Factorization of 630

The prime factorization of 630 is the way of expressing its prime factors in the product form.

Prime Factorization: 2 x 3 x 3 x 5 x 7

In this article, we will learn about the factors of 630 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

## What Are the Factors of 630?

The factors of 630 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, and 630. These numbers are the factors as they do not leave any remainder when divided by 630.

The factors of 630 are classified as prime numbers and composite numbers. The prime factors of the number 630 can be determined using the prime factorization technique.

## How To Find the Factors of 630?

You can find the factors of 630 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 630, create a list containing the numbers that are exactly divisible by 630 with zero remainders. One important thing to note is that 1 and 630 are 630’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 630 are determined as follows:

$\dfrac{630}{1} = 630$

$\dfrac{630}{2} = 315$

$\dfrac{630}{3} = 210$

$\dfrac{630}{5} = 126$

$\dfrac{630}{6} = 105$

$\dfrac{630}{7} = 90$

$\dfrac{630}{9} = 70$

$\dfrac{630}{10} = 63$

$\dfrac{630}{14} = 45$

$\dfrac{630}{15} = 42$

$\dfrac{630}{18} = 35$

$\dfrac{630}{21} = 30$

Therefore, 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, and 630 are the factors of 630.

### Total Number of Factors of 630

For 630, there are twenty-four positive factors and twenty-four negative ones. So in total, there are forty-eight factors of 630.

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 630 is given as:

Factorization of 630 is 1 x 2 x 3$^2$ x 5 x 7.

The exponent of 1, 2, 5, and 7 is 1. The exponent of 3 is 2.

Adding 1 to each and multiplying them together results in 48.

Therefore, the total number of factors of 630 is 48. 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 630 by Prime Factorization

The number 630 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 630 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 630, 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 630 can be expressed as:

630 = 2 x 3 x 3 x 5 x 7

## Factors of 630 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 630, the factor pairs can be found as:

1 x 630 = 630

2 x 315 = 630

3 x 210 = 630

5 x 126 = 630

6 x 105 = 630

7 x 90 = 630

9 x 70 = 630

10 x 63 = 630

14 x 45 = 630

15 x 42 = 630

18 x 35 = 630

21 x 30 = 630

The possible factor pairs of 630 are given as (1, 630), (2, 315), (3, 210), (5, 126), (6, 105), (7, 90), (9, 70), (10, 63), (14, 45), (15, 42), (18, 35), and (21, 30).

All these numbers in pairs, when multiplied, give 630 as the product.

The negative factor pairs of 630 are given as:

-1 x -630 = 630

-2 x -315 = 630

-3 x -210 = 630

-5 x -126 = 630

-6 x -105 = 630

-7 x -90 = 630

-9 x -70 = 630

-10 x -63 = 630

-14 x -45 = 630

-15 x -42 = 630

-18 x -35 = 630

-21 x -30 = 630

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, -5, -6, -7, -9, -10, -14, -15, -18, -21, -30, -35, -42, -45, -63, -70, -90, -105, -126, -210, -315, and -630 are called negative factors of 630.

## Factors of 630 Solved Examples

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

### Example 1

How many factors of 630 are there?

### Solution

The total number of Factors of 630 is twenty-four.

Factors of 630 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, and 630.

### Example 2

Find the factors of 630 using prime factorization.

### Solution

The prime factorization of 630 is given as:

630 $\div$ 2 = 315

315 $\div$ 3 = 105

105 $\div$ 3 = 35

35 $\div$ 5 = 7

7 $\div$ 7 = 1

So the prime factorization of 630 can be written as:

2 x 3 x 3 x 5 x 7 = 630