What % of the first 15 whole numbers have exactly 4 distinct whole number divisors? (1, 2, 3, and 6 are the four distinct divisors of 6)

what % of the first 10 whole numbers are prime? (remember, a prime number has only 1 and itself as a factor.)

what % of the first 10 whole numbers are perfect squares?

When a natural number is expressed as a product of two other natural numbers, those other numbers are factors of the original number. For example, two factors of 12 are 3 and 4, because 3 • 4 = 12.

When one number can be divided by another number with no remainder, we say the first number is divisible by the other number. For example, 20 is divisible by 4 (). If a number is divisible by another number, it is also a multiple of that number. For example, 20 is divisible by 4, so 20 is a multiple of 4.

A Prime Number can be divided evenly only by 1 or itself.
And it must be a whole number greater than 1.

But 6 can be divided evenly by 1, 2, 3 and 6 so it is NOT a prime number (it is a composite number).

Let me explain ...

Some whole numbers can be divided up evenly, and some can't!

6 can be divided evenly by 2, or by 3:

6 = 2 × 3

Like this:

But 7 cannot be divided up evenly:

And we give them names:

So 6 is Composite, but 7 is Prime.

 Many mathematical operations have an inverse, or opposite, operation. Subtraction is the opposite of addition, division is the inverse of multiplication, and so on. Squaring, which we learned about in a previous lesson (exponents), has an inverse too, called "finding the square root." Remember, the square of a number is that number times itself. The perfect squares are the squares of the whole numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 …

The square root of a number, n, written

 is the number that gives n when multiplied by itself. For example,

because 10 x 10 = 100

Examples

Here are the square roots of all the perfect squares from 1 to 100.

Finding square roots of of numbers that aren't perfect squares without a calculator

1. Estimate - first, get as close as you can by finding two perfect square roots your number is between.

2. Divide - divide your number by one of those square roots.

3. Average - take the average of the result of step 2 and the root.

4. Use the result of step 3 to repeat steps 2 and 3 until you have a number that is accurate enough for you.

Example: Calculate the square root of 10 () to 2 decimal places.

1. Find the two perfect square numbers it lies between.

Solution:
32 = 9 and 42 = 16, so  lies between 3 and 4.

2. Divide 10 by 3. 10/3 = 3.33 (you can round off your answer)

3. Average 3.33 and 3. (3.33 + 3)/2 = 3.1667

Repeat step 2: 10/3.1667 = 3.1579
Repeat step 3: Average 3.1579 and 3.1667. (3.1579 + 3.1667)/2 = 3.1623

Try the answer --> Is 3.1623 squared equal to 10? 3.1623 x 3.1623 = 10.0001

If this is accurate enough for you, you can stop! Otherwise, you can repeat steps 2 and 3.

Note: There are a number of ways to calculate square roots without a calculator. This is only one of them.

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