Divisors of 490

When we talk about numbers, one important concept is divisors. Divisors are the numbers that can divide another number evenly, leaving no remainder. Understanding divisors helps us break down numbers and see how they relate to each other. This article will explain what divisors are, how to find them, and specifically look at the divisors of the number 490.

To start, let’s look at the concept of division. When we divide one number by another, we are trying to see how many times the second number (called the divisor) fits into the first number (called the dividend). The result we get from this division is called the quotient. For example, when we divide the number 490 by 10, we have:

490 / 10 = 49

In this case, 490 is the dividend, 10 is the divisor, and 49 is the quotient.

Now, let’s go step-by-step to find the divisors of 490. We will divide 490 by every whole number starting from 1 all the way up to 490 itself. If we find a whole number result (meaning the division has no remainder), then that whole number is a divisor of 490.

Here’s how we can calculate the divisors of 490:

1. Start with 1:
   490 / 1 = 490 (Whole number, so 1 is a divisor)

2. Next, try 2:
   490 / 2 = 245 (Whole number, so 2 is a divisor)

3. Now try 3:
   490 / 3 = 163.33 (Not a whole number, so 3 is not a divisor)

4. Try 4:
   490 / 4 = 122.5 (Not a whole number, so 4 is not a divisor)

5. Try 5:
   490 / 5 = 98 (Whole number, so 5 is a divisor)

6. Now 6:
   490 / 6 = 81.67 (Not a whole number, so 6 is not a divisor)

7. Try 7:
   490 / 7 = 70 (Whole number, so 7 is a divisor)

8. Next, 8:
   490 / 8 = 61.25 (Not a whole number, so 8 is not a divisor)

9. Try 9:
   490 / 9 = 54.44 (Not a whole number, so 9 is not a divisor)

10. Finally, try 10:
    490 / 10 = 49 (Whole number, so 10 is a divisor)

At this point, we’ve checked many numbers. The divisors we found so far are 1, 2, 5, 7, and 10. We can continue this process all the way up to 490, but to keep it brief, we will summarize the full list of divisors.

After checking all numbers from 1 to 490, the divisors of 490 are:

1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, and 490.

In conclusion, the complete list of all the divisors of 490 is:

Divisors of 490: 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 490.

Understanding divisors is crucial in areas like number theory and can also be helpful in simplifying fractions, finding least common multiples, and other mathematical concepts.