# Factors of 34

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

#### How to find factors of a number

 1.   Find factors of 34 using Division Method 2.   Find factors of 34 using Prime Factorization 3.   Find factors of 34 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 34

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

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

#### 2. Steps to find factors of 34 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 34 using the division method, follow these steps:

• Step 1. Start dividing 34 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 34, which is 2. Divide 34 by 2 to obtain the quotient (17).
34 ÷ 2 = 17
• Step 3. Repeat step 1 with the obtained quotient (17).
17 ÷ 17 = 1

So, the prime factorization of 34 is, 34 = 2 x 17.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 34 as shown below:

So, the prime factorization of 34 is, 34 = 2 x 17.

#### 3. Find factors of 34 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 34 would be the two numbers which, when multiplied, give 34 as the result.

The following table represents the calculation of factors of 34 in pairs:

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

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 34. They are called negative pair factors.

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

#### How can we define factors?

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

#### Properties of factors

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

• Which is the smallest prime factor of 34?

The smallest prime factor of 34 is 2.

• Is 34 a whole number?

Yes 34 is a whole number.

• What are the prime factors of 34?

The factors of 34 are 1, 2, 17, 34.
Prime factors of 34 are 2, 17.

• What two numbers make 34?

Two numbers that make 34 are 2 and 17.

• What are multiples of 34?

First five multiples of 34 are 68, 102, 136, 170.

• What is the sum of all factors of 34?

The sum of all factors of 34 is 54.

• What are five multiples of 34?

First five multiples of 34 are 68, 102, 136, 170, 204.

• Is 34 a perfect square?

No 34 is not a perfect square.

• What is the greatest prime factors of 34?

The greatest prime factor of 34 is 17.

#### Examples of Factors

How many factors are there for 34?

Factors of 34 are 1, 2, 17, 34.
So there are in total 4 factors.

Kevin has been asked to write 3 factor(s) of 34. Can you predict the answer?

3 factor(s) of 34 are 1, 2, 17.

Sammy is puzzled while calculating the prime factors of 34. Can you help him find them?

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

What is prime factorization of 34?

Prime factorization of 34 is 2 x 17 = 2 x 17.

Ariel has been assigned the task to find the product of all the prime factors of 34. Can you help her?

Prime factors of 34 are 2, 17.
Hence, the product of prime factors of 34.

Can you help Rubel to find out the product of the even factors of 34?

Factors of 34 are 1, 2, 17, 34.
Even factors of 34 are 2, 34.
Hence, product of even factors of 34 is; 2 x 34 = 68.

Joy wants to calculate mean of all the factors of 34. Help him in finding the mean of 34.

Factors of 34 are 1, 2, 17, 34.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 34 is 1 + 2 + 17 + 34 = 54.
Hence, the mean of factors of 34 is 54 ÷ 4 = 13.50.