Divisors of 420

Divisors are special numbers that can evenly divide another number without leaving any remainder. In other words, if you divide one number by another and the answer is a whole number, the second number is a divisor of the first. Understanding divisors is important because they help us recognize patterns in numbers, solve mathematical problems, and even understand concepts in higher math.

To understand divisors better, we first need to know about division. Let’s break it down using the terms involved:

• Dividend: This is the number you want to divide. For example, in our case, the dividend is 420.
• Divisor: This is the number you are dividing by. For example, if we divide 420 by 1, then 1 is the divisor.
• Quotient: This is the result of the division. So if we divide 420 by 1, the quotient will be 420.

In formula form:
420 / 1 = 420
In this example, 420 is the dividend, 1 is the divisor, and 420 is also the quotient.

Now, let’s move on to how we can find out the divisors of the number 420. The idea is to divide 420 by every whole number starting from 1 up to 420 itself. If the result (the quotient) is a whole number (meaning it has no decimal places), then that whole number is a divisor of 420.

Here’s a step-by-step guide to calculate the divisors of 420:

1. Start with 1 and divide 420 by 1.
2. Then, divide 420 by 2.
3. Continue this process, increasing your divisor by 1 each time, up to 420.

Let’s perform the calculations:

1. 420 / 1 = 420 (whole number)
2. 420 / 2 = 210 (whole number)
3. 420 / 3 = 140 (whole number)
4. 420 / 4 = 105 (whole number)
5. 420 / 5 = 84 (whole number)
6. 420 / 6 = 70 (whole number)
7. 420 / 7 = 60 (whole number)
8. 420 / 8 = 52.5 (not a whole number)
9. 420 / 9 = 46.67 (not a whole number)
10. 420 / 10 = 42 (whole number)

We can see from our calculations that the numbers 1, 2, 3, 4, 5, 6, 7, and 10 give us whole number quotients. When we reached 8 and 9, they did not produce whole numbers, so they are not divisors. Continuing this process would yield more divisors, but for the sake of simplicity, we’ll stop here.

Now, let’s summarize the results:

• The divisors of 420 found so far are: 1, 2, 3, 4, 5, 6, 7, 10, etc.

To conclude, here is a complete list of all the divisors of 420:
1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, and 420.

Understanding divisors helps us to break numbers down into smaller, manageable parts, and recognizing these can simplify many mathematical tasks!