# Factors of 630

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

#### How to find factors of a number

 1.   Find factors of 630 using Division Method 2.   Find factors of 630 using Prime Factorization 3.   Find factors of 630 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 630

• Divide 630 by 1: 630 ÷ 1 : Remainder = 0
• Divide 630 by 2: 630 ÷ 2 : Remainder = 0
• Divide 630 by 3: 630 ÷ 3 : Remainder = 0
• Divide 630 by 5: 630 ÷ 5 : Remainder = 0
• Divide 630 by 6: 630 ÷ 6 : Remainder = 0
• Divide 630 by 7: 630 ÷ 7 : Remainder = 0
• Divide 630 by 9: 630 ÷ 9 : Remainder = 0
• Divide 630 by 10: 630 ÷ 10 : Remainder = 0
• Divide 630 by 14: 630 ÷ 14 : Remainder = 0
• Divide 630 by 15: 630 ÷ 15 : Remainder = 0
• Divide 630 by 18: 630 ÷ 18 : Remainder = 0
• Divide 630 by 21: 630 ÷ 21 : Remainder = 0
• Divide 630 by 30: 630 ÷ 30 : Remainder = 0
• Divide 630 by 35: 630 ÷ 35 : Remainder = 0
• Divide 630 by 42: 630 ÷ 42 : Remainder = 0
• Divide 630 by 45: 630 ÷ 45 : Remainder = 0
• Divide 630 by 63: 630 ÷ 63 : Remainder = 0
• Divide 630 by 70: 630 ÷ 70 : Remainder = 0
• Divide 630 by 90: 630 ÷ 90 : Remainder = 0
• Divide 630 by 105: 630 ÷ 105 : Remainder = 0
• Divide 630 by 126: 630 ÷ 126 : Remainder = 0
• Divide 630 by 210: 630 ÷ 210 : Remainder = 0
• Divide 630 by 315: 630 ÷ 315 : Remainder = 0
• Divide 630 by 630: 630 ÷ 630 : Remainder = 0

Hence, 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

#### 2. Steps to find factors of 630 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 630 using the division method, follow these steps:

• Step 1. Start dividing 630 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 630, which is 2. Divide 630 by 2 to obtain the quotient (315).
630 ÷ 2 = 315
• Step 3. Repeat step 1 with the obtained quotient (315).
315 ÷ 3 = 105
105 ÷ 3 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1

So, the prime factorization of 630 is, 630 = 2 x 3 x 3 x 5 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 630 as shown below:

So, the prime factorization of 630 is, 630 = 2 x 3 x 3 x 5 x 7.

#### 3. Find factors of 630 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 630 would be the two numbers which, when multiplied, give 630 as the result.

The following table represents the calculation of factors of 630 in pairs:

Factor Pair Pair Factorization
1 and 630 1 x 630 = 630
2 and 315 2 x 315 = 630
3 and 210 3 x 210 = 630
5 and 126 5 x 126 = 630
6 and 105 6 x 105 = 630
7 and 90 7 x 90 = 630
9 and 70 9 x 70 = 630
10 and 63 10 x 63 = 630
14 and 45 14 x 45 = 630
15 and 42 15 x 42 = 630
18 and 35 18 x 35 = 630
21 and 30 21 x 30 = 630

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 630. They are called negative pair factors.

Hence, the negative pairs of 630 would be ( -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 ) .

#### What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 630 is a factor of itself.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, 630 are exact divisors of 630.
• 1 is a factor of every number. Eg. 1 is a factor of 630.
• Every number is a factor of zero (0), since 630 x 0 = 0.

• Which is the smallest prime factor of 630?

Smallest prime factor of 630 is 2.

• Is 630 a perfect square?

No 630 is not a perfect square.

• What are five multiples of 630?

First five multiples of 630 are 1260, 1890, 2520, 3150, 3780.

• What is prime factorization of 630?

Prime factorization of 630 is 2 x 3 x 3 x 5 x 7.

• What are factors of 630?

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, 630.

• How do you find factors of a negative number? ( eg. -630 )?

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, -630.

• Is 630 a whole number?

Yes 630 is a whole number.

• Which is greatest factor of 630?

The greatest factor of 630 is 315.

• What are the prime 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, 630.
Prime factors of 630 are 2, 3, 3, 5, 7.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 630. Can you help her?

Prime factors of 630 are 2, 3, 3, 5, 7.
Hence, the product of prime factors of 210.

Can you help Rubel to find out the product of the even factors of 630?

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, 630.
Even factors of 630 are 2, 6, 10, 14, 18, 30, 42, 70, 90, 126, 210, 630.
Hence, product of even factors of 630 is; 2 x 6 x 10 x 14 x 18 x 30 x 42 x 70 x 90 x 126 x 210 x 630 = 4001504141376000000.

Joy wants to calculate mean of all the factors of 630. Help him in finding the mean of 630.

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, 630.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 630 is 1 + 2 + 3 + 5 + 6 + 7 + 9 + 10 + 14 + 15 + 18 + 21 + 30 + 35 + 42 + 45 + 63 + 70 + 90 + 105 + 126 + 210 + 315 + 630 = 1872.
Hence, the mean of factors of 630 is 1872 ÷ 24 = 78.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 630? Help her in writing all the factors.

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

How many factors are there for 630?

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, 630.
So there are in total 24 factors.

Joey wants to write all the prime factors of 630 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 630 are 2, 3, 3, 5, 7.
So in exponential form it can be written as 2 x 32 x 5 x 7.

Kevin has been asked to write 23 factor(s) of 630. Can you predict the answer?

23 factor(s) 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.