When we talk about the divisors of a number, we mean the numbers that can be multiplied together to produce the given number. For example, if we have the number 18, its divisors are the numbers that you can divide 18 by to get a whole number without any leftovers. Understanding divisors is helpful in many areas of math, such as fractions, ratios, and even solving equations. In this article, we’ll explore the divisors of the number 18 step-by-step.
To understand divisors better, we need to know a little about division. Division is a mathematical operation where we separate a total amount (called the dividend) into equal parts. The number we divide by is called the divisor, and the result we get is called the quotient. For example, in the division of 18 by 6, we can say that:
18 / 6 = 3
Here, 18 is the dividend, 6 is the divisor, and 3 is the quotient. This means if we take 18 and divide it into groups of 6, we would get 3 groups.
Now, to find the divisors of 18, we will divide 18 by every whole number starting from 1 all the way up to 18. If the result is a whole number, that means we have found a divisor.
Let’s go through the steps of finding the divisors of 18:
1. Start with 1. Divide 18 by 1:
– 18 / 1 = 18 (Whole number, so 1 is a divisor)
2. Next, try 2. Divide 18 by 2:
– 18 / 2 = 9 (Whole number, so 2 is a divisor)
3. Now, try 3. Divide 18 by 3:
– 18 / 3 = 6 (Whole number, so 3 is a divisor)
4. Next, try 4. Divide 18 by 4:
– 18 / 4 = 4.5 (Not a whole number, so 4 is not a divisor)
5. Continue with 5. Divide 18 by 5:
– 18 / 5 = 3.6 (Not a whole number, so 5 is not a divisor)
6. Next, try 6. Divide 18 by 6:
– 18 / 6 = 3 (Whole number, so 6 is a divisor)
7. Next, try 7. Divide 18 by 7:
– 18 / 7 = 2.57 (Not a whole number, so 7 is not a divisor)
8. Now, try 8. Divide 18 by 8:
– 18 / 8 = 2.25 (Not a whole number, so 8 is not a divisor)
9. Next, try 9. Divide 18 by 9:
– 18 / 9 = 2 (Whole number, so 9 is a divisor)
10. Finally, we check 18. Divide by 18:
– 18 / 18 = 1 (Whole number, so 18 is a divisor)
Now, let’s put together the results of our division calculations:
– 18 / 1 = 18 (1 is a divisor)
– 18 / 2 = 9 (2 is a divisor)
– 18 / 3 = 6 (3 is a divisor)
– 18 / 4 = 4.5 (4 is NOT a divisor)
– 18 / 5 = 3.6 (5 is NOT a divisor)
– 18 / 6 = 3 (6 is a divisor)
– 18 / 7 = 2.57 (7 is NOT a divisor)
– 18 / 8 = 2.25 (8 is NOT a divisor)
– 18 / 9 = 2 (9 is a divisor)
– 18 / 18 = 1 (18 is a divisor)
Now, looking back, we can compile all the found divisors of 18 into a neat list. The divisors of 18 are:
– 1
– 2
– 3
– 6
– 9
– 18
In conclusion, the divisors of the number 18 are 1, 2, 3, 6, 9, and 18. These numbers can divide 18 evenly, meaning there are no leftovers! Understanding these concepts is fundamental in math and can help with more advanced topics later on.