Textbook p9 #2:
The Prime factorisation of a number is 2^4 X 3^5 X 7^2 X 11.
Write down 3 factors of the number that are greater than 100.
(Hint: 16 X 11 = 176, which is a factor.)
My Answer: 2673, 539 and 23814
2^4 X 3^5 X 7^2 X 11= 2X2X2X2X3X3X3X3X3X7X7X11
Since the hint given is taking 16 times 11 to get the factor, then I guessed other factors could be calculated using 243 and 49 times 11 respectively.
So we have, 243 X 11=2673 and 49 X 11=539
Then I used the calculator to calculate the answer for 2X2X2X2X3X3X3X3X3X7X7X11 which is 2095632 and then I used the calculator to double check that both 2673 and 539 are factors for 2095632, which means my guess was correct.
Now, I have to find one more factor for this question. I used 2X2X2 (Please note that I used 2X2X2X2 to times 11 the previous time but now I am using 2X2X2 to times 11)times 11 and the answer is 88. So from here I know 88 is a factor of 2095632, but since it is not more than 100, I used 2095632 to divide it and got the result 23814.
After doing the homework, I realise that using the prime factorization, we are able to get the original number given and to find the factors and the highest common factors. :)
Textbook p9 #26:
The Prime factorisation of two numbers are 2 X 3^2 X 7^3 X 13 and3 X 7^2 X 13^3 X 17 .
Write down 3 common factors of the numbers.
My Answer: 3, 7 and 13
Prime number 3, 7 and 13 are present in the two prime factorisations and so these three numbers are the 3 common factors. :)