Factors Of 34 | With Easy Division and Prime Factorization

Factors Of 34

An integer factor of 34 is a number that divides the original number evenly, resulting in a whole number as a quotient. The number 34 has more than two factors since it is a composite number.

The factors and multiples of 34 are different from each other. In comparison, factors of a number divide the original number, whereas multiples are divisible by the original. In this case, 34 is both a factor and multiple.

Let’s go on to learn how to find the prime factors and pair factors of 34.

How to Find Factors of 34?

Numbers that divide 34 are called factors. You will also get the original number when finding the factors, we must divide the original number by natural numbers until the quotient is 1.

Our first step is to divide 34 by the smallest natural number, 1.

• 34 ÷ 1 = 34
• 34 ÷ 2 = 17
• 34 ÷ 17 = 2
• 34 ÷ 34 = 1

Accordingly, the factors of 34:

1, 2, 17, and 34.

What are the factors of -34?

Factors of -34: -1, -2, -17, and -34.

Multiplying two numbers to get the product -34 gives us the following:

-34 x  1 =  -34

34 x -1 =  -34

-17 x  2 = -34

17 x  -2 = -34

Therefore,  we have two possible pairs of factors of -34 as (-34 x  1), (34 x -1), (-17 x  2), and (17 x  -2).

Pair Factors of 34

Using the product of the two numbers, we can find the pair factors of 34.

Positive Pair Factors 

• 1 × 34 = 34
• 2 × 17 = 34

Consequently, the positive pair factors are (1, 34) and (2, 17).

Negative Pair Factors 

When you multiply 34 by its negative pair factors, you will also get the original number. Thus,

• -1 × -34 = 34
• -2 × -17 = 34

As a result, the negative pair factors are (-1, -34) and (-2, -17).

Prime Factorization of 34

A prime factor is a number that has only two factors. Typical examples include 2, 3, 5, 7, 11, etc. As we are looking for prime factors for 34, we need to determine whether that prime number is completely divisible by 34. 

So, we’ll start by dividing 34 by the smallest prime factor, 2.

Step 1:

Divide 34 by the smallest prime number.

34/2 = 17

Step 2:

Since 17 is a prime number, it can only be divided by 17.

17/17 = 1

Step 3:

No more division can be made. Therefore, 2 and 7 will be considered the prime factors of 34.

Prime factorization of 34 = 2 x 17

Solved Examples

Emma is giving out chocolates at her birthday party in her class. How many students are present if there are 34 chocolates and each gets two?

Number of chocolates = 34

Number of chocolates each student gets = 2

Therefore, number of students = 34/2 = 17

Calculate the sum of all the factors of 34.

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

Sum = 1+2+17+34 = 54

As a result, 54 is the required sum.

What are 33 and 101’s common factors?

Accordingly, the factors are

33 → 1, 3, 11, and 33

The factors of 101 = 1 and 101.

As a result, 33 and 101 have the same common factor of 1.

What are 34, 39, and 24’s common factors?

Accordingly, the factors are

Factors of 39 are 1, 3, 13, and 39.

34 has 1, 2, 17, and 34

Factors of 24 = 1, 2, 3, 4, 6, 8, 12, and 24.

Therefore 34, 39, and 24 have 1 common factor.

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