Factors of 34
2026-02-28 19:03 Diff
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Last updated on December 11, 2025

Do you know how number tricks work? Most of the number tricks work because of the unique characteristics of each number, i.e., factors. A factor of a number is any number that can evenly divide the number. For distributing objects, we use factors in our daily life.

What are the factors of 34.

The numbers which can evenly divide 34 are the factors of 34. 1, 2, 17, and 34 are the factors of 34.

Negative factors of 34: The negative factors of 34 are the negative counterparts of the positive factors. -1, -2, -17, and -34 are the negative factors of 34.

Prime factors of 34: A prime number is a number which has only two factors, i.e., 1 and the number itself.
2 and  17 are the prime factors of 34.

Prime factorization of 34: The process of splitting a number into smaller prime numbers is prime factorization. Here, the product of prime numbers is the number itself.


The prime factorization of 34 is 21 × 171
 

How to find the factors of 34

Factors of a number is a number which can evenly divide the number. Some methods which are used to find the factor of a 34 are,

  • Multiplication method
  • Division method
  • Prime factors and prime factorization
  • Factor tree
     

Finding factors using multiplication method:

In the multiplication method a pair of numbers are identified, the product of multiplying the number is 34. 


Step 1: Find the numbers whose product is 34

.
1 × 34 = 34


2 × 17 = 34

Step 2: List them as pairs

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

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Finding factors by division method

In the division method, we need to check which number can evenly divide 34. 

Let’s check the factors of 34 using division method

34 ÷ 1 = 34


34 ÷ 2 = 17

So, the factors are 1, 2, 17, and 34.
 

Prime factors and prime factorization

Prime numbers are the numbers which have only two factors. The process of breaking down a large number into a smaller prime number is prime factorization. 


To find the factors of a number prime factorization, we need to follow these steps

Step 1: The given number needs to be divided with the smallest prime number.

Step 2: Now, we need to divide the remainder in step 1 with the prime number. The process is continued till the remainder is a prime number.

   Let's use the prime factorization method to find the factors of 34.

The prime factors of 34 are 2 and 17.

2, 3, 5, 7, 11, 13, 17,… are the prime numbers. 

Step 1: Checking the divisibility by 2: 34 is an even number, so, it is divisible by 2.

34 ÷ 2 = 17.

Step 2: Now, the remainder is 17 which is a prime number. 

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

Factor tree

The Pictorial representation of factors of a number. It is in the form of a tree where the given number is split into branches which represent all the factors. 

The factor tree of 34:

Factor pair

A pair of factors of a number. The product of those numbers is the number itself. Factor pairs can be both positive and negative.

Positive pair factors: (1, 34), (2, 17).


Negative pair factors: (-1, -34), (-2, -17).
 

Common mistakes and how to avoid them in factors of 34

While finding the factors of any numbers, students tend to make mistakes. Mostly they tend to repeat the same error. Here is a list of some common mistakes and the ways to avoid them.
 

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Problem 1

Eliot planned to give cookies to his friends on his birthday. If he invited 17 friends to the birthday party, and each of them gets 2 cookies, then what is the total number of cookies Eliot has?

Okay, lets begin

Eliot has 34 cookies with him.
 

Explanation

Number of friends Eliot has = 17


The number of cookies each of them got = 2


Total number of cookies = number of friends × number of cookies each got


So the total number of cookies = 17 × 2 = 3 4
 

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Problem 2

What are the common factors of 34 and 30?

Okay, lets begin

The common factors are 1 and 2.
 

Explanation

The factors of 34 are 1, 2, 17, 34 and the factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. Let's Now identify the common numbers from the factors. Here the common factors are 1 and 2.
 

Well explained 👍

Problem 3

What is the LCM of 34 and 85?

Okay, lets begin

The LCM of 34 and 85 is 170.

Explanation

The product of the highest power of each prime factor of each number is the LCM of two numbers. Prime factorization of 34 and 85 is 21 × 171 and 51 × 171 respectively. So, the LCM is 21 × 51 × 171 = 2 × 5 × 17 = 170.
 

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Problem 4

What is the GCF of 34 and 51?

Okay, lets begin

The GCF of 34 and 51 is 17.

Explanation

GCF of two numbers is the product of common prime factors of each number. The prime factor of 34 is 21 × 171 and prime factor of 51 is 31 × 171. Here the common factor is 171, so the GCF is 17.
 

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FAQs on factors of 34

1.What two numbers make 34?

The numbers that make 34 are the number when multiplied, the product is 34. So, the numbers are (1, 34) and (2, 17).

2.What are the multiples of 34?

The multiples of 34 are 34, 68, 102, 136, 170, 204, 238, 272, 306, and 340.

3.Is 34 a multiple of 17?

Yes, 34 is a multiple of 17. Because 34 is evenly divisible by 17. 
 

4.Differentiate factors and multiples?

A factor of a number is a number which can evenly divide the number. Whereas a multiple of a number is the product of the number and a whole number.
 

5.What are the factors of 36?

 The factors of 36 are 1, 2, 3, 4, 6, 9, 18, 36.

Important glossaries for factors of 34

  • Prime number: Any numbers which has only two factors are the prime numbers
  • Composite numbers: The number which has more than two factors
  • Remainder: The value left after dividing a number by another number. For example, 1 is the remainder when we divide 5 by 2.
  • Product: The product of any number is the result of multiplying the number.
     

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Fun Fact

: She loves to read number jokes and games.