Maths How To with Anita

# What are the Factors of 34? (3 simple methods)

Need to know the factors of 34? You are in the right place!

As a math teacher since 2007, I love helping students have aha moments. Finding the factors of a number needs to become a quick skill like multiplication and division, so I have a few tips for you.

I’ll show you a variety of methods to find the factors of 34 as well as any other number so you can apply the best method that you like.

## What are the factors of 34?

Factors are numbers that divide into another number exactly. In other words, the answer to a division problem with no remainder. With that in mind, let’s look at the factors of 34.

Since 34 is an even number it is a composite number and has more than 2 factors.

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

## How to find the factors of 34

There are a few methods you can use to find the Factors of 34. I’ll show you 3 different methods:

### Method 1: Use a Factor Tree

A factor tree can be created by starting with the number you are trying to find the factors of. In this case, we will use 34.

Think of 2 numbers (not including 1 and 34) that multiply together to result in a product of 34.

Write these below the branches under 34.

If any of these numbers are prime numbers, circle them in red and stop drawing branches under them.

If any of these numbers are composite numbers draw another 2 branches underneath and continue until you get to 2 prime numbers.

Here is the factor tree for 34:

### Method 2: Use a calculator

A calculator can be used to quickly check if a number is a factor of 34 by seeing if the answer is a whole number or has a remainder.

If the answer is a whole number, then both the divisor and the quotient are factors of 34.

Start by dividing by 2, then 3, 4, etc until you get to the next factor and then you know to stop checking.

For example, using your calculator enter 34 ÷ 2. The answer is 17 a whole number. So both 2 and 17 are factors of 34.

Next enter 34 ÷ 3. The answer is not a whole number so 3 is not a factor of 34.

Continue testing every whole number until 16, whole number just before 17.

### Method 3: Use the Divisibility Rules.

The divisibility rules are a set of guidelines that can be followed to help determine if a number is a factor of another number.

Here are the divisibility rules for 2, 3, 4, 5, 6, 9 & 10.

2: A number is divisible by 2 if the last digit is 0, 2, 4, 6 or 8.

3: A number is divisible by 3 if the sum of all the digits is divisible by 3.

4: A number is divisible by 4 if the last 2 digits form a number that is divisible by 4.

5: A number is divisible by 5 if the last digit is 0 or 5.

6: A number is divisible by 6 if it is divisible by 2 and 3.

9: A number is divisible by 9 if the sum of all the digits is divisible by 9.

10: A number is divisible by 10 if the last digit is 0.

Let’s use the divisibility rules to find the factors of 34.

We’ll start with 2 since it’s the first prime number.

34 is divisible by 2 since the last digit is 4.

So, 2 is a factor of 34.

Next, we’ll check 3 using the divisibility rule for 3.

The sum of all the digits in 34 is 7 which is not divisible by 3. So, 3 is not a factor of 34.

We’ll check 4 next using the divisibility rule for 4.

The last 2 digits in 34 are 34 which is not divisible by 4. So, 4 is not a factor of 34.

We’ll check 5 next using the divisibility rule for 5.

The last digit in 34 is 4 which is not 0 or 5. So, 5 is not a factor of 34.

We’ll check 6 next since it’s the next number and it’s divisible by 2 & 3.

We already know that 2 is a factor of 34 and we just determined that 3 is not a factor of 34. So, 6 is not a factor of 34.

We’ll check 9 next using the divisibility rule for 9.

The sum of all the digits in 34 is 7 which is not divisible by 9. So, 9 is not a factor of 34.

Lastly, we’ll check 10 using the divisibility rule for 10.

The last digit in 34 is 4 which is not 0. So, 10 is not a factor of 34.

So the only factors of 34 are 1, 2, 17 & 34.

## What is the prime factorization of 34?

The prime factorization of 34 is 2 x 17.

Both 2 and 17 are prime numbers and they are both factors of 34.

## How to find the prime factors of 34

To find the prime factors of 34, you need to find the factors of 34 that are also prime numbers.

I like to draw a factor tree to do this.

The only prime factors of 34 are 2 and 17.

## What are the factors pairs of 34

Factors pairs of 34 are 1 x 34 & 2 x 17. These Factor Pairs multiply together to equal 34.

I like to draw a factor rainbow to find the factor pairs for any number.

Watch me draw a factor rainbow for 90 here.

## What is the product of prime factors of 34?

Product is another name for multiplication so we can write 34 as the product of the prime factors like this: 34 = 2 x 17.

## Negative factors of 34

Negative factors pairs of 34 would be -1 x -34 & -2 x -17.

Both factors must be negative to result in a product of positive 34.

## FAQs

### How many factors does 34 have?

34 has 4 factors; 1,2, 17 & 34

1+2+17+34 = 54

## Conclusion

The best way to get better at finding factors and prime factors is by practicing! You can use a factor tree, make a factor rainbow, or use a calculator.

When you’re trying to find the prime factorization of a number, keep in mind that any even number has 2 as one of its factors. Additionally, all negative numbers have corresponding positive factor pairs.

Now it’s time for you to test your skills! Try finding the prime factorization of 34 using each method.

## Further factors

Learn more about the factors of other numbers here.