Remainders of nb

1044 * 1047 1050 * 1053

Now 1044 = (2^2)(3^2)(29)
1044 % 33 = [(4.9)%33][29%33]=[3.29]%33=87%33=21

1047=1044+3
Therefore, 1047%33=24

1050=1044+6
Therefore, 1050%33=27

1053=1044+9
Therefore, 1053%33=30

Therefore [1044 * 1047 1050 * 1053]%33 = [21.24.27.30]%33
or (504%33)(810%33)= [9(18)]%33=30

Answer: 30

Does anyone know a quicker way of solving this?

What is the remainder when 1044 * 1047 * 1050 * 1053 is divided by 33?

first divide 1044 by 33 you will get ramainder 21
1047 is 3 more so remainder will be 21+3=24
remainder with 1050 will give remainder 24+3=27
remainder with 1053 will be 27+3=30

now we can say 1044 * 1047 * 1050 * 1053 divided by 33
we get 21*24*27*30
we can also say 21*24*27*30 as(-12*-9*6*3)
36*54 divided by 33 (-12*-3)(-9*-6)

3* 21 divided by 33
63 divided by 33 remainder 30 answer
if this conceot understood remainder problem wiill be cakewalk

what is the remainder when (1023+21)(1023+24)(1023+27)(1023+30) is divided by 33?
OR
what is the remainder when (21)(24)(27)(30) is divided by 33?
OR
what is the remainder when (-12)(-9)(-6)(-3) is divided by 33?
OR
what is the remainder when (36)(54) is divided by 33?
OR
what is the remainder when (3)(21) is divided by 33?
OR
what is the remainder when (63) is divided by 33?
OR
what is the remainder when (66-3) is divided by 33?

The remainder is 30.

amising6 wrote: we get 21*24*27*30
we can also say 21*24*27*30 as (-12*-9*6*3)
36*54 divided by 33 (-12*-3)(-9*-6)

Ahh! Didn't realize this! thanks!

How do you get (-12)(-9)(-6)(-3)?

francoisph wrote:How do you get (-12)(-9)(-6)(-3)?

33-12 = 21,
33-9=24
33-6=27
33-3=30

So we can interchange 21 with -12.

Let me know if its not clear..

I missed one step

how do you get ?
36*54 divided by 33 (-12*-3)(-9*-6)
3* 21 divided by 33

francoisph wrote:I missed one step

how do you get ?
36*54 divided by 33 (-12*-3)(-9*-6)
3* 21 divided by 33

Reminder of 36*54 divided by 33 is same as
Reminder of 3* 21 divided by 33 because 36%33=3, 54%33=21

Hope this helps!!

ok,

guys is it sometimes that you did in american school ?problem of remainders

I never did in high school, the negative remainder concept
o:)