Factors of 170
2026-02-28 17:41 Diff
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Last updated on December 11, 2025

Factors of any number are the dividers or multipliers that can divide the number fully and can be multiplied together to produce the given product, 170. Do you know, factors form the basic approach to solve some general mathematical procedures? This article will give you the insights of factors of 170.

What are the Factors of 170?

The factors of 170 or the numbers which divide 170 exactly are:


1,2,5,10,17,34,85, and 170.


Negative factors of 170: -1,-2,-5,-10,-17,-34,-85,-170.


Prime factors of 170: 2,5,17


Prime factorization of 170: 2×5×17


The sum of factors of 170: 1+2+5+10+17+34+85+170= 324
 

How to Find the Factors of 170

For finding factors of 170, we will be learning these below-mentioned methods:

  • Multiplication Method
  • Division Method
  • Prime Factor and Prime Factorization
  • Factor Tree

Finding Factors using Multiplication Methods

This particular method often finds the pair of factors which, on multiplication together, produces 170. Let us find the pairs which, on multiplication, yields 170.


1×170=170


2×85=170


5×34=170


10×17=170


So, factors of 170 are: 1,2,5,10,17,34,85, and 170.
 

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Finding Factors using Division Method

The division method finds the factors that evenly divides the given number 170. In this process, we have to divide 170 by all possible natural numbers less than 170 and check.


1,2,5,10,17,34,85, and 170 are the only factors that the number 170 has. So to verify the factors of 170 using the division method, we just need to divide 170 by each factor.


170/1 =170


170/2=85


170/5=34


170/10=17


170/17=10


170/34=5


170/85=2


170/170=1

Prime Factors and Prime Factorization

Prime Factorization is the easiest process to find prime factors. It decomposes 170 into a product of its prime integers.


Prime Factors of 170: 2,5,17.


Prime Factorization of 170: 2×5×17
 

Factor tree

The number 170 is written on top and two branches are extended.


Fill in those branches with a factor pair of the number above, i.e., 170.


Continue this process until each branch ends with a prime factor (number).


The first two branches of the factor tree of 170 are 2 and 85, then proceeding to 85, we get 5 and 17. So, now the factor tree for 170 is achieved. 

Factor Pairs

Positive pair factors:   (1,170), (2,85), (5,34), (10,17).


Negative pair factors:  (-1,-170), (-2,-85), (-5,-34), (-10,-17).
 

Common Mistakes and How to Avoid Them in Factors of 170

Solving problems based on factors can, sometimes, lead to misconceptions among children. Let us check what the common errors are and how to avoid them.
 

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Problem 1

Find the GCF of 85 and 170

Okay, lets begin

Factors of 170: 1,2,5,10,17,34,85,170


Factors of 85: 1,5,17,85


Common factors of 85 and 170: 1,5,17,85


So, the Greatest Common Factor of 85 and 170 is 85.


Answer: 85
 

Explanation

We first listed out the factors of 85 and 170 and then found the common factors and then identified the greatest common factor from the common list. 

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Problem 2

Find the smallest number which, when divided by 17,34 and 85, leaves a remainder 3 in each case.

Okay, lets begin

 First finding the LCM of 17,34,85


Prime factorization of 17 =17×1


Prime factorization of 34 = 17×2


Prime factorization of 85 = 5×17


LCM of 17,34,85 = 17×2×5=170


The smallest number which, when divided by 17,34 and 85, leaves a remainder 3 in each case is = LCM + 3 = 170+3 =173


Answer: 173
 

Explanation

First find the LCM and just add the remainder with that to get the smallest number.
 

Well explained 👍

Problem 3

The area of a rectangle is 170 square units. If the length is 34 units, then what is the measure of its width?

Okay, lets begin

Area of rectangle: 170 sq units


Factors of 170: 1,2,5,10,17,34,85,170


We know that the area of a rectangle is the product of its length and breadth.


Given, length= 34 units


There exists a factor pair of 170, which is (5,34). Hence, width is 5 units. Let’s check it through the formula for area.
So, length×width = area


⇒ 34 × width = 170


⇒ width = 170/34 = 5


Answer: 5 units
 

Explanation

Used the concept of factor pairs for 170 and rechecked using the formula for finding area of a rectangle.
 

Well explained 👍

Problem 4

Find the smallest number that is divisible by 2,5,34.

Okay, lets begin

Prime factorization of 2: 2×1.


Prime factorization of 5: 5×1


Prime factorization of 34: 17×2

LCM of 2,5,34: 2×5×17 = 170


Answer: 170 is the smallest number which is divisible by 2,5, and 34.
 

Explanation

To find the smallest number which is divisible by 2,5,34, we need to find the LCM of these numbers.
 

Well explained 👍

Problem 5

What is the sum of the factors of 170 and 175?

Okay, lets begin

Factors of 170: 1,2,5,10,17,34,85,170


Sum of the factors: 1+2+5+10+17+34+85+170= 324

Factors of 175: 1,5,7,25,35,175
 

Explanation

Sum of the factors: 1+5+7+25+35+175=248
 

Well explained 👍

FAQs on Factors of 170

1.What is the factor tree of 170?

The number 170 is written on top and two branches are extended. Fill in those branches with a factor pair of the number above, i.e., 170. Continue this process until each branch ends with a prime factor (number). The first two branches of the factor tree of 170 are 2 and 85, then proceeding to 85, we get 5 and 17. So, now the factor tree for 170 is achieved.
 

2.What is the LCM of 170 and 238?

Prime factorization of 170: 2×5×17


Prime factorization of 238: 2×7×17


LCM of 170 and 238: 2×5×7×17 = 1190. 
 

3. List out the first 5 multiples of 170.

 170 has infinite multiples. Let us list out the first five of it: 170, 340, 510, 680, 850,... Try to list out five more multiples of 170.

4.Is 170 a multiple of 10?

 Let us check if 170 is a multiple of 10. We can test this by dividing 170 by 10, and see if it leaves a remainder other than 0. 170/10=17. Hence, 170 is a multiple of 10.

5.What are the 5 multiples of 17?

17 has infinite multiples. Let us list out the first five of it: 17, 34, 51, 68, 85,... Try to list out five more multiples of 17.
 

Important Glossaries for Factors of 170

  • Multipliers - Number which multiplies or a number by which another number is multiplied.
  • Dividers - A number that divides.
  • Prime Factorization - It involves factoring the number into its prime factors.
  • Prime factors - These are the prime numbers which on multiplication together results into the original number whose prime factors are to be obtained.
  • Composite numbers - These are numbers having more than two factors.
  • Multiple - It is a product of the given number and any other integer.
     

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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.