# Factors of 578

Factors of 578 are 1, 2, 17, 34, 289, and 578

#### How to find factors of a number

 1.   Find factors of 578 using Division Method 2.   Find factors of 578 using Prime Factorization 3.   Find factors of 578 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 578

• Divide 578 by 1: 578 ÷ 1 : Remainder = 0
• Divide 578 by 2: 578 ÷ 2 : Remainder = 0
• Divide 578 by 17: 578 ÷ 17 : Remainder = 0
• Divide 578 by 34: 578 ÷ 34 : Remainder = 0
• Divide 578 by 289: 578 ÷ 289 : Remainder = 0
• Divide 578 by 578: 578 ÷ 578 : Remainder = 0

Hence, Factors of 578 are 1, 2, 17, 34, 289, and 578

#### 2. Steps to find factors of 578 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 578 using the division method, follow these steps:

• Step 1. Start dividing 578 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 578, which is 2. Divide 578 by 2 to obtain the quotient (289).
578 ÷ 2 = 289
• Step 3. Repeat step 1 with the obtained quotient (289).
289 ÷ 17 = 17
17 ÷ 17 = 1

So, the prime factorization of 578 is, 578 = 2 x 17 x 17.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 578 as shown below:

So, the prime factorization of 578 is, 578 = 2 x 17 x 17.

#### 3. Find factors of 578 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 578 would be the two numbers which, when multiplied, give 578 as the result.

The following table represents the calculation of factors of 578 in pairs:

Factor Pair Pair Factorization
1 and 578 1 x 578 = 578
2 and 289 2 x 289 = 578
17 and 34 17 x 34 = 578

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 578. They are called negative pair factors.

Hence, the negative pairs of 578 would be ( -1 , -578 ) , ( -2 , -289 ) and ( -17 , -34 ) .

#### What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 578 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, 17, 34, 289, 578 are exact divisors of 578.
• 1 is a factor of every number. Eg. 1 is a factor of 578.
• Every number is a factor of zero (0), since 578 x 0 = 0.

• What two numbers make 578?

Two numbers that make 578 are 2 and 289.

• What is prime factorization of 578?

Prime factorization of 578 is 2 x 17 x 17.

• Write some multiples of 578?

First five multiples of 578 are 1156, 1734, 2312, 2890.

• Which is the smallest prime factor of 578?

The smallest prime factor of 578 is 2.

• Is 578 a perfect square?

No 578 is not a perfect square.

• What is the sum of all factors of 578?

The sum of all factors of 578 is 921.

• What are factors of 578?

Factors of 578 are 1, 2, 17, 34, 289, 578.

• How do you find factors of a negative number? ( eg. -578 )?

Factors of -578 are -1, -2, -17, -34, -289, -578.

• Is 578 a whole number?

Yes 578 is a whole number.

#### Examples of Factors

Joy wants to calculate mean of all the factors of 578. Help him in finding the mean of 578.

Factors of 578 are 1, 2, 17, 34, 289, 578.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 578 is 1 + 2 + 17 + 34 + 289 + 578 = 921.
Hence, the mean of factors of 578 is 921 ÷ 6 = 153.50.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 578? Help her in writing all the factors.

Positive factors are 1, 2, 17, 34, 289, 578.
Negative factors are -1, -2, -17, -34, -289, -578.

Joey wants to write all the prime factors of 578 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 578 are 2, 17, 17.
So in exponential form it can be written as 2 x 172.

Kevin has been asked to write 5 factor(s) of 578. Can you predict the answer?

5 factor(s) of 578 are 1, 2, 17, 34, 289.

Sammy is puzzled while calculating the prime factors of 578. Can you help him find them?

Factors of 578 are 1, 2, 17, 34, 289, 578.
Prime factors of 578 are 2, 17, 17

What is prime factorization of 578?

Prime factorization of 578 is 2 x 17 x 17 = 2 x 172.

Can you help Rubel to find out the product of the even factors of 578?

Factors of 578 are 1, 2, 17, 34, 289, 578.
Even factors of 578 are 2, 34, 578.
Hence, product of even factors of 578 is; 2 x 34 x 578 = 39304.