Prime Factorisation

Textbook Page 9 #25

The prime factorisation of a number is 24 x 35 x 72 x 11. Write down 3 factors of the number that are greater than 100.

24x35x72x11=(2x2x2x2) x (3x3x3x3x3) x (7x7) x 11

=16 x 243 x 49 x 11

=2 095 632

2 095 632=1 x 2 095 632

=2 x 1 047 816

=3 x 698 544... ...(so on and so forth)

How do we get 3 factors of 2 095 632? We cannot possibly be dividing until we get our answer. We should take the factors from the index notation and multiply them to get our answer.

We can take 243 x 7(49/7=7), and we get 1701. (Check: 2 095 632/1701=1232[correct]) We also know that 1232, which is larger than 100, is also a factor of 2 095 632. Then, we take 1232/2 to get 616. We first assume it is a factor and we then check it. Can 2 095 632 be divided 616? Yes, and we will get 3402, another factor of 2 095 632.

So, the answer is 1701, 1232 and 616.

Textbook Page 9 #26

The prime factorisation of two numbers are 2 x 32 x 73 x 13 and 3 x 72 x 133 x 17. Write down 3 common factors of each numbers.

First, we find out WHAT exactly are the numbers?

2 x 32 x 73 x 13= 2 x 9 x 343 x 13

= 80 262

3 x 72 x 133 x 17= 3 x 49 x 2197 x 17

= 5 490 303

What do 5 490 303 and 80 262 have in common? Well, they will surely have common factors. Obviously, they will have 1 as their common factor. Then, we try to work out the answer like this:

5 490 303= 1 x 5 490 303

= 3 x 1 830 101

= 7 x 784 329

= 13 x 422 331

= 17 x 322 959

80 262= 1 x 80 262

= 2 x 40 131

= 3 x 26754

= 6 x 13 377

= 7 x 11 466

So, the answer is 1, 3 and 7.