What are the factors of ?
These are the integers which can be evenly divided into ; they can be expressed as either individual factors or as factor pairs. In this case, we present them both ways. This is mathematical decomposition of a particular number. While usually a positive integer, take note of the comments below about negative numbers.
What is the prime factorization of ?
A prime factorization is the result of factoring a number into a set of components which every member is a prime number. This is generally written by showing as a product of its prime factors. For , this result would be:= 2 x 2 x 3 x 17
(this is also known as the prime factorisation; the smallest prime number in this series is described as the smallest prime factor)
Is a composite number?
Yes! is a composite number. It is the product of two positive numbers other than 1 and itself.
Is a square number?
No! is not a square number. The square root of this number () is not an integer.
How many factors does have?
This number has 12 factors: 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, ,
More specifically, shown as pairs
(1*) (2*) (3*68) (4*51) (6*34) (12*17) (17*12) (34*6) (51*4) (68*3) (*2) (*1)
What is the greatest common factor of and another number?
The greatest common factor of two numbers can be determined by comparing the prime factorization (factorisation in some texts) of the two numbers and taking the highest common prime factor. If there is no common factor, the gcf is 1. This is also referred to as a highest common factor and is part of the common prime factors of two numbers. It is the largest factor (largest number) the two numbers share as a prime factor. The least common factor (smallest number in common) of any pair of integers is 1.
How can you find the least common mulitiple of and another number?
We have a least common multiple calculator here The solution is the lowest common multiple of two numbers.
What is a factor tree
A factor tree is a graphic representation of the possible factors of a numbers and their sub-factors. It is designed to simplify factorization. It is created by finding the factors of a number, then finding the factors of the factors of a number. The process continues recursively until you've derived a bunch of prime factors, which is the the prime factorization of the original number. In constructing the tree, be sure to remember the second item in a factor pair.
How do you find the factors of negative numbers? (eg. )
To find the factors of , find all the positive factors (see above) and then duplicate them by adding a minus sign before each one (effectively multiplying them by -1). This addresses negative factors. (handling negative integers)
Is a whole number?
What are the divisibility rules?
Divisibility refers to a given integer number being divisible for a given divisor. The divisibility rule are a shorthand system to determined what is or isn't divisible. This includes rules about odd number and even number factors. This example is intended to allow the student to estimate the status of a given number without computation.
Factors of Other Numbers
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Why is the prime factorization of written as 22 x 31 x 171?
What is prime factorization?
Prime factorization or prime factor decomposition is the process of finding which prime numbers can be multiplied together to make the original number.
Finding the prime factors of
To find the prime factors, you start by dividing the number by the first prime number, which is 2. If there is not a remainder, meaning you can divide evenly, then 2 is a factor of the number. Continue dividing by 2 until you cannot divide evenly anymore. Write down how many 2's you were able to divide by evenly. Now try dividing by the next prime factor, which is 3. The goal is to get to a quotient of 1.
If it doesn't make sense yet, let's try it
Here are the first several prime factors: 2, 3, 5, 7, 11, 13, 17, 19, 23,
Let's start by dividing by 2
÷ 2 = - No remainder! 2 is one of the factors!
÷ 2 = 51 - No remainder! 2 is one of the factors!
51 ÷ 2 = - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
51 ÷ 3 = 17 - No remainder! 3 is one of the factors!
17 ÷ 3 = - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
17 ÷ 5 = - This has a remainder. 5 is not a factor.
17 ÷ 7 = - This has a remainder. 7 is not a factor.
17 ÷ 11 = - This has a remainder. 11 is not a factor.
Keep trying increasingly larger numbers until you find one that divides evenly.
17 ÷ 17 = 1 - No remainder! 17 is one of the factors!
The orange divisor(s) above are the prime factors of the number If we put all of it together we have the factors 2 x 2 x 3 x 17 = It can also be written in exponential form as 22 x 31 x 171.
Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number
More Prime Factorization Examples
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FAQs on Factors of
What are the Factors of ?
The factors of are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, , and its negative factors are -1, -2, -3, -4, -6, , , , , , ,
What is the Sum of all the Factors of ?
Sum of all factors of = (22 + 1 - 1)/(2 - 1) × (31 + 1 - 1)/(3 - 1) × (171 + 1 - 1)/(17 - 1) =
What are Pair Factors of ?
The pair factors of are (1, ), (2, ), (3, 68), (4, 51), (6, 34), (12, 17).
What is the Greatest Common Factor of and ?
The factors of and are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, , and 1, 2, 4, 7, 14, 28, 49, 98, respectively.
Common factors of and are [1, 2, 4].
Hence, the GCF of and is 4.
What are the Common Factors of and 57?
Since, the factors of are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, , and the factors of 57 are 1, 3, 19,
Hence, [1, 3] are the common factors of and
Here we have a collection of all the information you may need about the Prime Factors of We will give you the definition of Prime Factors of , show you how to find the Prime Factors of (Prime Factorization of ) by creating a Prime Factor Tree of , tell you how many Prime Factors of there are, and we will show you the Product of Prime Factors of
Prime Factors of definition
First note that prime numbers are all positive integers that can only be evenly divided by 1 and itself. Prime Factors of are all the prime numbers that when multiplied together equal
How to find the Prime Factors of
The process of finding the Prime Factors of is called Prime Factorization of To get the Prime Factors of , you divide by the smallest prime number possible. Then you take the result from that and divide that by the smallest prime number. Repeat this process until you end up with 1.
This Prime Factorization process creates what we call the Prime Factor Tree of See illustration below.
All the prime numbers that are used to divide in the Prime Factor Tree are the Prime Factors of Here is the math to illustrate:
÷ 2 =
÷ 2 = 51
51 ÷ 3 = 17
17 ÷ 17 = 1
Again, all the prime numbers you used to divide above are the Prime Factors of Thus, the Prime Factors of are:
2, 2, 3,
How many Prime Factors of ?
When we count the number of prime numbers above, we find that has a total of 4 Prime Factors.
Product of Prime Factors of
The Prime Factors of are unique to When you multiply all the Prime Factors of together it will result in This is called the Product of Prime Factors of The Product of Prime Factors of is:
2 × 2 × 3 × 17 =
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Prime Factors of
We hope this step-by-step tutorial to teach you about Prime Factors of was helpful. Do you want a test? If so, try to find the Prime Factors of the next number on our list and then check your answer here.
Of prime 204 factors
- is a composite number.
- Prime factorization: = 2 × 2 × 3 × 17, which can be written = 2² × 3 × 17
- The exponents in the prime factorization are 2, 1, and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1)(1 + 1) = 3 x 2 x 2 = Therefore has exactly 12 factors.
- Factors of 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, ,
- Factor pairs: = 1 x , 2 x , 3 x 68, 4 x 51, 6 x 34, or 12 x 17
- Taking the factor pair with the largest square number factor, we get √ = (√4)(√51) = 2√51 ≈ 14.5659987996
Excel file of puzzles and previous week’s factor solutions: 12 Factors
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