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Factors

Factors of 34 | Prime Factorization of 34 | Factor Tree of 34

Written by Prerit Jain

Updated on: 18 Aug 2023

Contents

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Factors of 34 | Prime Factorization of 34 | Factor Tree of 34

Factors of 34 | Prime Factorization of 34 | Factor Tree of 34

Factors of 34: There are a total of four factors of the number 34. Factors of 34 are 1, 2, 17, and 34. Factors are those numbers that divide a particular number evenly. The numbers 1, 2, 17, and 34 divide 34 fully, without a remainder.

The factors of a number can be either positive or negative. They can also be written as pairs. This means that multiplying the set of two factors in pairs gives the original product (34).

In this article, let us discuss how to find factors of 34, its prime factorization, and factor trees with solved examples. Keep reading to learn more.

What Are the Factors of 34?

The factors of 34 are those numbers that can divide another number evenly without leaving any remainder. The factors can usually be both positive and negative. The number 34 also has both positive and negative factors.

Factors of 34: 1, 2, 17 and 34
Negative Factors of 34: –1, -2, -17 and -34
Prime Factorization of 34: 2 X 17
Pair Factors of 34: (1, 34); (2, 17)
Prime Factors of 34: 2, 17
Sum of Factors of 34: 54
Sum of Prime Factors of 34: 19
Factors of 34

What Are the Factors of 34 in Pairs?

A pair factor of 34 is a combination of two numbers when multiplied together gives the product of the original number (34). These pairs can also be written in positive and negative pairs as shown below:

Positive Pair Factors of 34

The positive pair factors of 34 are (1, 34) and (2, 17).

Positive Pair Factors of 34

 

Negative Pair Factors of 34

The negative pair factors of 34 are (-1, -34) and (-2, -17).

Negative Pair Factors of 34

 

How To Find Factors of 34 Through Division Method?

To find the factors of 34 we can employ many methods. Here, we are using the division method. This method needs you to multiply a sequence of natural integers by 34. The numbers that divide the 34 completely without leaving any remainder are known as the factors of 34. The detailed steps for finding factors of 34 using the division method are below:

34 ÷ 1 = 34

34 ÷ 2 = 17

34 ÷ 17 = 2

34 ÷ 34 = 1

Thus, we can see that 1, 2, 17, and 34 are the numbers that do not leave any remainder when divided by 34. This proves that they are the factors of 34. 

What Is the Prime Factorization of 34?

In order to perform prime factorization, we must first check if the given number is a prime number. If it is a prime number, then it will have only two factors: 1 and 34. If the given number is a composite number, then it will have more than two factors.
Since 34 is the composite number, we have more than two factors. Hence, we can use the prime factorization method to find the factors of 34.
The steps to find prime factors of 34 using the prime factorization method are given below:

Step 1: Divide 34 by the smallest prime number that can divide evenly. The smallest prime number that can divide 34 is 2. So, 34 ÷ 2 = 17

Step 2: Now, divide the number 17 (quotient) by the next smallest prime number. But since 17 is a prime number, it can only be divided by 1 and 17. So, 17 ÷ 17 = 1. The quotient is 1. We can see that 1 cannot be divided further. So, the prime factors of 34 are 2 X 17. We can also write it down as 2 and 17, as they are both prime numbers.

Image representation of the prime factorization of 34:

Prime Factorization of 34

What is the Factor Tree of 34?

Students can also use the factor tree to find the prime factors of 34. In this method, we will place the number 34 at the top. Now, we will write down any one pair factors of the given number (34), as the branches of 34. We will split the pair of factors into factors. This will go on until the branches become prime numbers. Now, circling all the prime numbers will give us the prime factors of 34.

Step 1: Place the number 34 at the top of the factor tree. Let us branch out 34 into any of its factor pairs, that is, 2 and 17.

Step 2: Since 2 is a prime number, we can no longer separate it. 17 also happens to be a prime number, and it cannot be separated either. The branches in the factor tree will now be all the prime numbers.

There are many ways in which we can write the factor tree of 34. Below is an image representation of the factor tree of 34, choosing 2 and 17 as pair factors of 34.

Factor tree of 34

Solved Examples on Factors of 34:

Here are some solved examples of 34 factors:

What is the sum of all the factors of 34?
1, 2, 17, and 34 are the 34 factors.
1 + 2 + 17 + 34 = 54
Hence, 54 is the sum of all 34 factors.

What are the factors and prime factors of 34?
The factors of 34 are 1, 2, 17, and 34.
The prime factors of 34 are 2 and 17.

What’s the highest common factor between 102 and 34?
The factors of 102 are 1, 2, 3, 6, 17, 34, 51, and 102.
Factors of 34 are 1, 2, 17, and 34.
Hence, the common factors of 102 and 34 are 1, 2, 17, and 34.
The highest common factor between 102 and 34 is 34.

What’s the highest common factor between 17 and 34?
The factors of 17 are 1 and 17.
Factors of 34 are 1, 2, 17, and 34.
Hence, from the above, the common factors of 17 and 34 are 1 and 17.
The highest common factor between 17 and 34 is 17.

Is 204 a factor of 34?
No, but 204 is not a factor of 34.
204 ÷ 34 = 6.

What are the factors of -34?
The factors of -34 are -1, -2, -17, and -34.

What are the common factors of 85 and 34?
To find the common factors of 85 and 33, we need to find the factors of both 85 and 33.
Factors of 85: 1, 5, 17 and 85
Factors of 34: 1, 2, 17 and 34
Hence the common factors of 85 and 34 are 1 and 17.

What are all the factors of 34?
The factors of 34 are 1, 2, 17, and 34.

What are the factors of 34 that are composite?
Any number which has more than 2 factors is known as a composite number. The number which has more than 2 factors in factors of 34 is only 34.

What factors of 34 are multiples of 2?
The factors of 34 that are multiples of 2 are 2 and 34.
2 x 1 = 2
2 x 14 = 34.

How many factors of 34 are odd?
A total of 2 odd numbers are there in factors of 34 and they are 1 and 17.

What are the factors of 51 and 34?
The factors of 51 are 1, 3, 17, and 51.
The factors of 34 are 1, 2, 17, and 34.

How many factors are there for the number 34?
A total of 4 factors are there for the number 34 and are 1, 2, 17, and 34.

What factors of 34 are multiples of 2?
The factors of 34 that are multiples of 2 are 2 and 34.

How many pair factors are there in 34?
A total of 2 pairs are there in factors of 34.

What is the largest factor of 34?
The largest factor of 34 is 34.
The second largest factor of 34 is 17.

FAQs on Factors of 34

List all the factors of 34
1, 2, 17, and 34 are the 34 factors.

What are the composite factors of 34?
34 is the only composite factor of 34.
Composite factors are those that have more than 2 factors other than 1 and itself.

What are the factors of 34 in pairs?
(1, 34) and (2, 17) are the 34 factors of pairs.

What are the positive factors for 34?
1, 2, 17, and 34 are the positive factors for 34.

What are some of the multiples of 34? A multiple is a number that may be divided by another a certain number of times without a remainder.
The multiples of 34 are 34, 68, 102, 136, 170, 204, 238, 272, 306, and 340.

Now we have learned everything about the factors of 34. We hope this blog has proved useful and easy for you. If you have any more doubts, feel free to comment below. We will get back to you shortly.

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Prerit Jain

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