Question

Find a number between 800 and 900 which is divisible by 22, 33, and 66.

Answer 1

Prime Factorization of 22 = 2 × 11
Prime Factorization of 33 = 3 × 11
Prime Factorization of 66 = 2 × 3 × 11
For a number to be divisible by 22, 33 and 66, it should be divisible by 2, 3 and 11 also.
Now, the numbers between 800 and 900 which are divisible by 11 are
803, 814, 825, 836, 847, 858, 869, 880, 891
Out of these, the numbers which are divisible by 3 are
825, 858, 891
Now, the numbers which are divisible by 2 end with an even number. The only number which is divisible by 2 among these is 858.
So, 858 is the number which is divisible by 22, 33 and 66.