304 LearnersLast updated on May 26th, 2025
Factors of 85
Factors of any number are the whole numbers that can divide the number completely. Why are factors important to learn? For mathematical approaches, factors are used in organizing and bringing more efficiency to any task. In this article, let's learn how to solve factors 85 easily.
What are the Factors of 85?
Factors of 85 are those numbers that can divide 85 perfectly. The factors of 85 are:
1,5,17 and 85.
Negative factors of 85: -1, -5, -17, -85.
Prime factors of 85: 5,17
Prime factorization of 85: 5×17
The sum of factors of 85: 1+5+17+85 = 108
How to Find the Factors of 85
For finding factors of 85, 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 85. Let us find the pairs which, on multiplication, yields 85.
1×85=85
5×17=85
From this, we conclude that, factors of 85 are: 1,5,17, and 85.
Finding Factors using Division Method
The division method finds the numbers that evenly divides the given number 85. To find the factors of 85, we have to divide 85 by all possible natural numbers less than 85 and check.
1,5,17,85 are the only factors that the number 85 has. So to verify the factors of 85 using the division method, we just need to divide 85 by each factor.
85/1 =85
85/5 =17
85/17=5
85/85=1
Prime Factors and Prime Factorization
Prime Factorization is the easiest process to find prime factors. It decomposes 85 into a product of its prime integers.
- Prime Factors of 85: 5,17.
- Prime Factorization of 85: 5×17
Factor tree
The number 85 is written on top and two branches are extended.
Fill in those branches with a factor pair of the number above, i.e., 85.
Continue this process until each branch ends with a prime factor (number).
The first two branches of the factor tree of 85 are 5 and 17.
Factor Pairs:
Positive pair factors: (1,85), (5,17)
Negative pair factors: (-1,-85), (-5,-17).
Common Mistakes and How to Avoid Them in Factors of 85
Children quite often make silly mistakes while solving factors. Let us see what are the common errors to occur and how to avoid them.
Mistake 1
Misconception and confusion about factors with that of multiples.
Factors are way different from multiples. You need to understand it clearly that factors are integers which divide a given number evenly, and multiples are the products we get when the original number is multiplied with different numbers.
Factors of 85 Examples
Problem 1
The LCM of two numbers is 85 and their GCF is 5. If one of the numbers is 25, find the other.
Solution: We know that the product of two numbers is equal to the product of their GCF and LCM.
⇒ 25× x = 85×5
⇒ x =(85×5) / 25
⇒ x = 17
Answer: The other number is 17.
Explanation
Using the concept of the product of two numbers being equal to the product of their GCF and LCM, we solved it.
Problem 2
Find the simplest form of square root of 85.
√85 = √(5×17) = √85
Answer: The simplest form of square root of 85 is √85.
Explanation
Break down 85 into its product of its prime factor and find its square root by grouping a pair of factors at a time, leaving the remaining single factors under radical.
Problem 3
The area of a rectangle is 85 square units. If the length is 17 units, then what is the measure of its width?
Area of rectangle: 85 sq units
Factors of 85: 1,5,17,85
We know that the area of a rectangle is the product of its length and breadth.
Given, length= 17 units
There exists a factor pair of 85, which is (5,17). Hence, width is 5 units. Let’s check it through the formula for area.
So, length×width = area
⇒ 17 × width = 85
⇒ width = 85/17 = 5
Answer: 5 units
Explanation
Used the concept of factor pairs for 85 and rechecked using the formula for finding area of a rectangle.
Problem 4
Find the smallest number that is divisible by 5 and 85.
Prime factorization of 5: 5×1.
Prime factorization of 85: 5×17
LCM of 5 and 85: 5×17 = 85
Answer: 85 is the smallest number which is divisible by 5 and 85.
Explanation
To find the smallest number which is divisible by 5 and 85, we need to find the LCM of these numbers.
Problem 5
If a number is divisible by both 5 and 17, is it divisible by 85?
Yes, any number which is divisible by 5 and 17 is also divisible by 85, since 85 = 5×17
Answer: Yes
Explanation
Any number which is divisible by the factor 5 and factor 17 of 85, then it is also divisible by 85 because 85 is a product of 5 and 17.
FAQs on Factors of 85
1.Can 85 be divided evenly?
2.What is the factor tree of 85?
3.What is the highest common factor of 85?
4.Is 85 divisible by 3?
5.Is 85 a prime number or composite number?
6.How can children in Qatar use numbers in everyday life to understand Factors of 85?
7.What are some fun ways kids in Qatar can practice Factors of 85 with numbers?
8.What role do numbers and Factors of 85 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of 85 skills?
Important Glossaries for Factors of 85
- Ratio - Ratio of two numbers compares between them, how many times one number contains the other number. It is expressed as m:n, where m and n are two positive numbers whose ratio is to be shown.
- Factors - These are numbers that divide the given number without leaving any remainder or the remainder as 0.
- 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 Qatar
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.
