Question

15. (a) Find the greatest 4-digit number that is divisible by 5.
(b) Find all the numbers between 283 and 297 that are divisible by both 2 and 3.
16. Find the nrime fact​

Answer 1

Answer:

9990 is the biggest 4 digit number divisibly by both 5 and 10.

We have integers sharing a Common property for divisibility by 6 that ones place digit -2*tens place digit-2 *hundred place digit-2*thousand place digit….. gives an integer divisible by 6 then number also divisible by 6.

Here in 284:-4–2*8–2*2= -16 =2(mod6)

Similarly285, 286, 287 gives 3, 4, and 5 (mod6).

In this way 288 and 294 gives 0 (mod6).

We know that a number divisible by both 2 and 3 also divisible by 6.

So, required numbers are 288 and 294.

Examples of Prime Decomposition: Factors and Exponents

Prime factorization of 100 is 2 x 2 x 5 x 5 or 22 x 52

Prime factorization of 76 is 2 x 2 x 19 or 22 x 191

Prime factorization of 50 is 2 x 5 x 5 or 2 x 52

Prime factorization of 48 is 2 x 2 x 2 x 2 x 3 or 24 x 31

More items...

Answer 2

Answer:

a) 9990

b) 294 and 299 only