# Factors of 730

Factors of 730 are 1, 2, 5, 10, 73, 146, 365, and 730

#### How to find factors of a number

 1.   Find factors of 730 using Division Method 2.   Find factors of 730 using Prime Factorization 3.   Find factors of 730 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 730

• Divide 730 by 1: 730 ÷ 1 : Remainder = 0
• Divide 730 by 2: 730 ÷ 2 : Remainder = 0
• Divide 730 by 5: 730 ÷ 5 : Remainder = 0
• Divide 730 by 10: 730 ÷ 10 : Remainder = 0
• Divide 730 by 73: 730 ÷ 73 : Remainder = 0
• Divide 730 by 146: 730 ÷ 146 : Remainder = 0
• Divide 730 by 365: 730 ÷ 365 : Remainder = 0
• Divide 730 by 730: 730 ÷ 730 : Remainder = 0

Hence, Factors of 730 are 1, 2, 5, 10, 73, 146, 365, and 730

#### 2. Steps to find factors of 730 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 730 using the division method, follow these steps:

• Step 1. Start dividing 730 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 730, which is 2. Divide 730 by 2 to obtain the quotient (365).
730 ÷ 2 = 365
• Step 3. Repeat step 1 with the obtained quotient (365).
365 ÷ 5 = 73
73 ÷ 73 = 1

So, the prime factorization of 730 is, 730 = 2 x 5 x 73.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 730 as shown below:

So, the prime factorization of 730 is, 730 = 2 x 5 x 73.

#### 3. Find factors of 730 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 730 would be the two numbers which, when multiplied, give 730 as the result.

The following table represents the calculation of factors of 730 in pairs:

Factor Pair Pair Factorization
1 and 730 1 x 730 = 730
2 and 365 2 x 365 = 730
5 and 146 5 x 146 = 730
10 and 73 10 x 73 = 730

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 730. They are called negative pair factors.

Hence, the negative pairs of 730 would be ( -1 , -730 ) , ( -2 , -365 ) , ( -5 , -146 ) and ( -10 , -73 ) .

#### 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. 730 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, 5, 10, 73, 146, 365, 730 are exact divisors of 730.
• 1 is a factor of every number. Eg. 1 is a factor of 730.
• Every number is a factor of zero (0), since 730 x 0 = 0.

• What are the prime factors of 730?

The factors of 730 are 1, 2, 5, 10, 73, 146, 365, 730.
Prime factors of 730 are 2, 5, 73.

• What is the sum of all factors of 730?

The sum of all factors of 730 is 1332.

• What are the pair factors of 730?

Pair factors of 730 are (1,730), (2,365), (5,146), (10,73).

• What two numbers make 730?

Two numbers that make 730 are 2 and 365.

• What are multiples of 730?

First five multiples of 730 are 1460, 2190, 2920, 3650.

• Is 730 a perfect square?

No 730 is not a perfect square.

• Which is greatest factor of 730?

The greatest factor of 730 is 365.

• How do you factors of 730?

Factors of 730 are 1, 2, 5, 10, 73, 146, 365, 730.

• What are five multiples of 730?

First five multiples of 730 are 1460, 2190, 2920, 3650, 4380.

#### Examples of Factors

Can you help Rubel to find out the product of the even factors of 730?

Factors of 730 are 1, 2, 5, 10, 73, 146, 365, 730.
Even factors of 730 are 2, 10, 146, 730.
Hence, product of even factors of 730 is; 2 x 10 x 146 x 730 = 2131600.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 730? Help her in writing all the factors.

Positive factors are 1, 2, 5, 10, 73, 146, 365, 730.
Negative factors are -1, -2, -5, -10, -73, -146, -365, -730.

How many factors are there for 730?

Factors of 730 are 1, 2, 5, 10, 73, 146, 365, 730.
So there are in total 8 factors.

Sammy is puzzled while calculating the prime factors of 730. Can you help him find them?

Factors of 730 are 1, 2, 5, 10, 73, 146, 365, 730.
Prime factors of 730 are 2, 5, 73

Joey wants to write all the prime factors of 730 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 730 are 2, 5, 73.
So in exponential form it can be written as 2 x 5 x 73.

What is prime factorization of 730?

Prime factorization of 730 is 2 x 5 x 73 = 2 x 5 x 73.

Can you help Rubel to find out the product of the even factors of 730?

Factors of 730 are 1, 2, 5, 10, 73, 146, 365, 730.
Even factors of 730 are 2, 10, 146, 730.
Hence, product of even factors of 730 is; 2 x 10 x 146 x 730 = 2131600.