Divisors of 252

Divisors of a number are the integers that can divide that number without leaving a remainder. In simpler terms, if you can divide a number by another number and get a whole number as the answer, then that second number is a divisor of the first one. The purpose of this article is to help you understand what divisors are and how to find them, using the example of the number 252.

To understand divisors better, let’s first look at what division means. In a division problem, we have three important terms:

1. Dividend: This is the number that we want to divide. In our example, the dividend will be 252.
2. Divisor: This is the number we are dividing by. For instance, if we divide 252 by 3, then 3 is the divisor.
3. Quotient: This is the result we get after dividing the dividend by the divisor. Continuing with our example, 252 divided by 3 gives us 84, so 84 is the quotient.

So, using our example:
252 / 3 = 84

Now, let’s proceed to find the divisors of 252. To do this, we will divide 252 by each integer starting from 1 up to 252. We will check if the result is a whole number. If it is, we will note the divisor down.

Here’s the step-by-step guide:

1. Start with 1 and go up to 252.
2. For each integer (let’s call it d), divide 252 by d.
3. If 252 / d gives a whole number with no decimal, then d is a divisor of 252.

Now, let’s see the calculations:

• 252 / 1 = 252 (whole number, so 1 is a divisor)
• 252 / 2 = 126 (whole number, so 2 is a divisor)
• 252 / 3 = 84 (whole number, so 3 is a divisor)
• 252 / 4 = 63 (whole number, so 4 is a divisor)
• 252 / 5 = 50.4 (not a whole number, not a divisor)
• 252 / 6 = 42 (whole number, so 6 is a divisor)
• 252 / 7 = 36 (whole number, so 7 is a divisor)
• 252 / 8 = 31.5 (not a whole number, not a divisor)
• 252 / 9 = 28 (whole number, so 9 is a divisor)
• 252 / 10 = 25.2 (not a whole number, not a divisor)
• 252 / 11 = 22.909 (not a whole number, not a divisor)
• 252 / 12 = 21 (whole number, so 12 is a divisor)
• 252 / 13 = 19.384 (not a whole number, not a divisor)
• 252 / 14 = 18 (whole number, so 14 is a divisor)
• 252 / 15 = 16.8 (not a whole number, not a divisor)
• 252 / 16 = 15.75 (not a whole number, not a divisor)
• 252 / 17 = 14.823 (not a whole number, not a divisor)
• 252 / 18 = 14 (whole number, so 18 is a divisor)
• 252 / 19 = 13.263 (not a whole number, not a divisor)
• 252 / 21 = 12 (whole number, so 21 is a divisor)
• 252 / 22 = 11.454 (not a whole number, not a divisor)
• 252 / 24 = 10.5 (not a whole number, not a divisor)
• 252 / 28 = 9 (whole number, so 28 is a divisor)
• 252 / 36 = 7 (whole number, so 36 is a divisor)
• 252 / 42 = 6 (whole number, so 42 is a divisor)
• 252 / 63 = 4 (whole number, so 63 is a divisor)
• 252 / 84 = 3 (whole number, so 84 is a divisor)
• 252 / 126 = 2 (whole number, so 126 is a divisor)
• 252 / 252 = 1 (whole number, so 252 is a divisor)

From our calculations, we can see the divisors that produce whole numbers:

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252.

So, to conclude, this is the complete list of all divisors of 252:

Divisors of 252: 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252.

With this understanding, you are now able to find the divisors of any number using a similar approach!