DIY Challenge 3: Five numbers, one pattern
Try this for 5 different numbers and share your findings. Do you notice anything interesting? Why do you think is it happening?
Note: Please use a calculator if you feel the need.
What students worked out15
Student 1
I think the pattern here is that if you choose a number do the following steps the every time you divide you move down by a place value e.g I start with a 4 digit the after I divide I end up with a 3 digit then 2 digit
Student 1
Also that the 3 digit number that you think of then make it a 6 digit number then do the division it ends up with the same 3 digit number that you started with e.g 454 is my 3 digit no. I make it 454454 then 454454/7=64922 then 64922/11=5902 then 5902/13=454
Karanteacher
Why do you think this is happening?
Student 1
Because all the numbers that you divide are prime numbers
Student 1
For this problem
Student 2
WE WILL ALWAYS END UP WITH THE SAME NUMBER THAT WE STARTED WITH. IF I (for eg:) started with 274 the end number will also be 274 as
step 1 274
step 2 274274
step 3 [(274274*7)*11]*13 or 274274*1001
I have done the same trick before i have a math magic book
another thing
if the number is
2 DIGIT-101
3 DIGIT-1001
4 DIGIT-10001
5 DIGIT-100001
6 DIGIT-1000001Karanteacher
Interesting. Looks like there’s a small error in step 3. What do you think?
Student 11
Can’t find the reason, but I think that Rehan is right
Student 14
You end with the number you started with.
Student 14
Same as 77/11.
Student 3
6 digit no formed is 1001 times that of 3 digit no
and 7,11,13 are prime factors of 1001
so final answer comes sameStudent 15
sir the number gets divided so many times that it results in the number that we thought of like sir I took 555 and at the end the result was 555
Student 15
and sir i think its doing that because the number is divisible by 11 and there are other prime numbers dividing it to
Student 15
no sir
Student 9
If we multiply a 6 digit number by 7*11*13 or 1001 the answer would be the same number.