Factors of 18 are the list of integers that can be evenly divided into 18. It has a total of 6 factors of which 18 is the biggest factor and the positive factors of 18 are 1, 2, 3, 6, 9, and 18. The Pair Factors of 18 are (1, 18), (2, 9), and (3, 6) and its Prime Factors are 1, 2, 3, 6, 9, 18.
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Let us explore more about factors of 18 and ways to find them.
|1.||What Are the Factors of 18?|
|2.||How to Calculate Factors of 18?|
|3.||Factors of 18 in Pairs|
|5.||FAQs on Factors of 18|
What Are the Factors of 18?
Factors of a number are the numbers that divide the given number exactly without any remainder. According to the definition of factors, the factors of 18 are 1, 2, 3, 6, 9, and 18. So,18 is a composite number as it has more factors other than 1 and itself.
How to Calculate Factors of 18?
We can use different methods like the divisibility test, prime factorization, and the upside-down division method to calculate the factors of 18. In prime factorization, we express 18 as a product of its prime factors, and in the division method, we see which numbers divide 18 exactly without a remainder.
Let us calculate factors of 18 using the following two methods:Factors of 18 by prime factorization factor tree methodFactors of 18 by upside-down division method
Prime Factorization By Upside-Down Division Method
Prime factorization is expressing a number as a product of its prime factors.For example, factors of 6 are 1, 2, 3, 66 = 2 × 3So, the prime factors of 6 are 2 and 3.
The upside-down division got its name because the division symbol is flipped upside down.STEP 1: By using divisibility rules, we find out the smallest exact prime divisor (factor) of the given number. Here, 18 is an even number. So it is divisible by 2. In other words, 2 divides 18 with no remainder. Therefore, 2 is the smallest prime factor of 18.STEP 2: We divide the given number by its smallest factor other than 1 (prime factor), 18 ÷ 2 = 93 is the quotient, so we stop the process here. Therefore, 18 = 2 × 3 × 3
Prime Factorization by Factor Tree Method
First, we identify the two factors that give 18. 18 is the root of this factor tree.18 = × 6Here, 6 is a composite number. So it can be further factorized.6 = 3 × 2We continue this process until we are left with only prime numbers, i.e., till we cannot further factor the obtained numbers.We then circle all the prime numbers in the factor tree. Basically, we branch out 18 into its prime factors.
So, the prime factorization of 18 is 18= 2 × 3 × 3.
A factor tree is not unique for a given number. Instead of expressing 18 as 2 × 9, we can express 18 as 3 × 6. Here is a simple activity to try on your own. Instead of 2 × 9, if I had used 3 × 6, do you think we would get the same factors?Can you draw the factor tree with 3 and 6 as the branches?
Explore factors using illustrations and interactive examples
Factor pairs are the two numbers that, when multiplied, give the number 18.18 = 1 × 1818 = 2 × 918 = 3 × 6
Therefore, pair factors of 18 are (1,18), (2,9), and (3,6). A factor rainbow helps you find all of the factors. It is called a rainbow because all of the factor pairs connect to make a rainbow! Making a factor rainbow is quite easy.
Let’s try one:Find all of the factors for the number 18.Step I: Start with 1 and the number itself.Step II: Count up by ones to see if you can multiply two numbers together to get your target number.Step III: Stop when you can’t get any more numbers in between.Step IV: Connect the factor pairs.
In total, we have 3 factor pairs, i.e., there are 6 factors of 18: 1, 2, 3, 6, 9, 18.
We can have negative factors also for a given number.For example: Since the product of two negative numbers is positive <(-) × (-) = +>.(-1,-18) , (-2,-9), and (-3,-6) are also factor pairs of 18.But for now, let us focus on the positive factors in this article.With factors, we are only looking for whole numbers that are equal to or less than the original number.
Important Notes:Factors of a number are the numbers that divide the given number exactly without any remainder.18 is a composite number as it has more factors other than 1 and itself.Pair factors of 18 are (1,18), (2,9), and (3,6).1 is a factor of every number.The factor of a number is always less than or equal to the given number.Prime factorization is expressing the number as a product of its prime factors.
90 × 0.2= 18. Can we conclude (90, 0.2) as a factor pair of 18?Is the number of factors of a given number finite?Can the factor of a number be greater than the number itself?
Example 2: There are 18 people in a room together at a party. Everyone would like to take part in games during the party. What could be the possible sizes of groups we can break the people into so that no one is left out and everyone can play?
To solve this problem, we need to know the factors of 18.List them out: 1, 2, 3, 6, 9, 18.Let"s see how the factor pairs can help us.Factor pairs: (1,18), (2,9), (3,6)
The first pair, 1 and 18, doesn"t tell us much. It just means that we could have 1 group of 18.
The second pair tells us we could have 2 groups of 9 or 9 groups of 2.
The third pair tells us we could have 3 groups of 6 or 6 groups of 3.
Now we can see that there are three possible combinations for grouping the party guests: (1,18), (2,9), (3,6).
Example 3: Xin has a plot of land with an area of 18 sq. ft. He wants to break this plot of land into different equal-sized sections to plant different vegetables. In how many can he divide the plot?
The area of the rectangle is length × breadth.Given area = 18 square feetSo, the possible length and breadth are the factor pairs (as the product of these pairs is 18).
There are 3 possible ways. We can swap the dimensions of length and breadth according to the situation.
FAQs on Factors of 18
What are the Factors of 18?
The factors of 18 are 1, 2, 3, 6, 9, 18 and its negative factors are -1, -2, -3, -6, -9, -18.
What is the Greatest Common Factor of 18 and 13?
The factors of 18 are 1, 2, 3, 6, 9, 18 and the factors of 13 are 1, 13. 18 and 13 have only one common factor which is 1. This implies that 18 and 13 are co-prime.Hence, the Greatest Common Factor (GCF) of 18 and 13 is 1.
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What are the Common Factors of 18 and 7?
Since the factors of 18 are 1, 2, 3, 6, 9, 18, and factors of 7 are 1, 7. Hence, 18 and 7 have only one common factor which is 1. Therefore, 18 and 7 are co-prime.
What is the Sum of the Factors of 18?
All the Factors of 18 are 1, 2, 3, 6, 9, 18 and therefore the sum of all these factors is 1 + 2 + 3 + 6 + 9 + 18 = 39