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
2X2X2X2=16
3X3X3X3X3=243
7X7=49
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. :)
Lai Ziying
Hi Ziying
ReplyDeleteTextbook p9 #2:
You are right! Indeed, if you recall, when we do prime factorisation, it's 'breaking up' the composite into its simplest term. Hence, in the process of multiplying all the factors (in the index notation), you are working backwards and therefore reached the original number :D
Your answers are correct :D
Indeed, there are many possible answers.
One way is, find the composite number (that you did). Simply divide it by any of the prime factors (e.g. 2, 3, 7, 11), you will find another factor that's definitely larger than 100 :D
Textbook p9 #26:
The answers are correct.
Indeed, if we list down the factors, you will notice there are several ways to find the possible common factors (of which some are not prime factors).
Cheers!