finding roots composite numbers step 1: find all the factors of a number

Finding Roots

Composite Numbers

STEP 1:

Find all the factors of a numberFind all the factors of a number

Example: Say you want to find the factors of 8.

The factors of 8 are all the numbers that will divide into 8 evenly.(In other words, they are not decimals like 2.38 or 4.1)

So take the numbers from 1 to 8 and divide 8 by each of them.

1) 8

8) 8

2) 8 3) 8 4) 8

5) 8 6) 8 7) 8

What are factors and how do I find them?

8 4 2decimal

1decimaldecimal decimal

If you get an answer with a decimal in it, the number you divided by is not a factor of 8, so cross out these answers.

Now let’s look at the numbers that are left

1) 8 8) 82) 8 4) 88 4 2 1

The numbers on top are the factors of 8, factors: 8, 4, 2 and 1

But, did you notice that the numbers on the top and the numbers you divided by (on the left) are the same?

That’s because we are finding the factors two at a time,The number on the left and the number on top

are both factors of 8.

So to save time we don’t have to divide by every number from 1 to 8, we can go halfway and stop.

If we only have to find half of the factors, how do we know when we have gotten halfway and can stop?

1) Write the number with two little branches below it

82) Starting with ‘1 x 8’Write all the pairs of factors that divide evenly into 8 1 * 8

2 * 44 * 28 * 1

3) This is where theystart to repeat, STOP HERE!

You don’t need to write these repeating numbers down

If you write the factors of the number using the following system,you can see where your stopping point will be.

All the factors of 8 are right here in this little box.

Practice:Find the factors of the following numbers

12 32 81 481 * 122 * 63 * 4

1 * 322 * 164 * 8

1 * 813 * 279 * 9

1 * 482 * 243 * 164 * 126 * 87 * decimal

Here’s where thenumbers start to repeat 4 * 3, etc.

so stop here.

Factors of 12: 1, 2, 3, 4, 6, 12

5 * decimal6 * decimal7 * decimal8 * 4(repeat)

Make sure you check all the numbers up to the number on the bottom right, this is

where they start to repeat.

Factors of 32: 1, 2, 4, 8, 16, 32 Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Factors of 81: 1, 3, 9, 27, 81

You can stop heresince there are no

more numbersbetween these two

factors on the bottom

We can stop checking numbers

as soon as we reach

this number

Stop, since thenext number is 8

Read the factorsin this order

Down the left side Up

the right side

Step 2: Split the number into two factorsStep 2: Split the number into two factors

1 * 122 * 63 * 4

Use the splitting property to simplify the following:

1) Find all the pairs of factors-look for perfect squares2) Find the pair with the largest perfect square

3) Write this pair in the following order:

4 is a perfect square

4) Take the square root of the perfect number

Answer

This is a square root, so look for perfect squares






Answer


1 * 322 * 164 * 8

4 and 16 are perfect squares

1 * 813 * 279 * 9



1) Find all the pairs of factors-look for perfect squares


2) Double factors like this mean that the original numberwas a perfect square and this splitting process is unnecessary.

3) Take the square root of 81 (see perfect numbers chart)

Note: Checking for Prime numbers should also be done before tryingthe splitting process because prime numbers cannot be broken up at all.

Answer

Answer






Answer


4 and 16 are perfect squares

1 * 482 * 243 * 164 * 126 * 8



1) Find all the pairs of factors-look for perfect cubes2) Find the pair with the largest perfect cube


4) Take the cube root of the perfect number

Answer

This is a cube root, so look for perfect

cubes

27 is a perfect cube

1 * 1082 * 543 * 364 * 276 * 189 * 12

Practice Problems

finding roots composite numbers step 1: find all the factors of a number

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