Question

What is the prime factorization of 126

Answer 1

Were you taught any method for this?

Answer 2

Answer : 2 • 3^2 • 7

Answer 3

no I was not

Answer 4

Okay, then, let's just exhaust it ^^
Can you think of a number that you can divide 126 by?
Any number...

Answer 5

12

Answer 6

No... 126/12 = 10 with a remainder of 6...
There mustn't be any remainders...
also, stick to using primes...

Answer 7

2

Answer 8

Okay, good ^_^
What's 126 divided by 2?

Answer 9

63

Answer 10

Okay.
So let's keep that 2.
Now... any number that 63 can be divided by?

Answer 11

\[\Large 126 = 2\times 63\]
63 can be divided by...?

Answer 12

it can not be dvided by 2 right

Answer 13

Nope... it's not even...however, there ARE numbers you can divide it by (with no remainder, of course)

Answer 14

3

Answer 15

Okay, great, and what's 63 divided by 3?

Answer 16

21

Answer 17

Okay, let's recap then.
\[\Large 126 = 2\times \color{red}{63}= 2\times \color{red}{3\times 21}\]
So far so good?

Answer 18

okay

Answer 19

yes, sir

Answer 20

What about 21, then?
Can THAT be divided by anything?

Answer 21

3

Answer 22

That's right, and 21 divided by 3 is...?

Answer 23

7

Answer 24

Okay, so we get..
\[\Large 126 = 2\times 63 =2 \times 3 \times \color{green}{21}= 2 \times 3 \times \color{green}{3 \times 7}\]
Finally we have 7... can THAT be divided by anything?

Answer 25

no

Answer 26

Of course not, because 7 is prime ^_^
So, all these factors are prime, now, so THIS
\[\Large 126 = \color{blue}{2\times 3\times3 \times 7}\]
IS the prime factorisation of 126.

Get it? Got it? Good. ^_^

Answer 27

yes thank you