213 LearnersLast updated on May 26th, 2025
Factors of 170
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.
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.
Mistake 1
Factors might be larger than the given number.
Factors can never be larger than the given number, but multiples can be. You need to understand the concept that factors are integers which divide a given number perfectly, and multiples are the products we get when the original number is multiplied with different numbers.
Factors of 170 Examples
Problem 1
Find the GCF of 85 and 170
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.
Problem 2
Find the smallest number which, when divided by 17,34 and 85, leaves a remainder 3 in each case.
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.
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?
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.
Problem 4
Find the smallest number that is divisible by 2,5,34.
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.
Problem 5
What is the sum of the factors of 170 and 175?
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
FAQs on Factors of 170
1.What is the factor tree of 170?
2.What is the LCM of 170 and 238?
3. List out the first 5 multiples of 170.
4.Is 170 a multiple of 10?
5.What are the 5 multiples of 17?
6.How can children in Philippines use numbers in everyday life to understand Factors of 170?
7.What are some fun ways kids in Philippines can practice Factors of 170 with numbers?
8.What role do numbers and Factors of 170 play in helping children in Philippines develop problem-solving skills?
9.How can families in Philippines create number-rich environments to improve Factors of 170 skills?
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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About BrightChamps in Philippines
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.
