Entre los siguientes números, encuentre los que son múltiplos de 2, 3, 5 y 10: 235, 360, 487, 564, 681, 792, 854, 904.

Steps to Solve

1. Divisibility rule for 2

A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).

2. Divisibility rule for 3

A number is divisible by 3 if the sum of its digits is divisible by 3.

3. Divisibility rule for 5

A number is divisible by 5 if its last digit is 0 or 5.

4. Divisibility rule for 10

A number is divisible by 10 if its last digit is 0.

5. Check 235

Divisible by 5 (ends in 5). Not divisible by 2 or 10 (ends in 5). Sum of digits is $2+3+5 = 10$, which is not divisible by 3.

6. Check 360

Divisible by 2 (ends in 0). Divisible by 3 (sum of digits is $3+6+0 = 9$, which is divisible by 3). Divisible by 5 (ends in 0). Divisible by 10 (ends in 0).

7. Check 487

Not divisible by 2 (ends in 7). Not divisible by 5 or 10 (ends in 7). Sum of digits is $4+8+7 = 19$, which is not divisible by 3.

8. Check 564

Divisible by 2 (ends in 4). Sum of digits is $5+6+4 = 15$, which is divisible by 3. Not divisible by 5 or 10 (ends in 4).

9. Check 681

Not divisible by 2,5 or 10 because it ends in 1. Sum of digits is $6+8+1 = 15$, which is divisible by 3.

10. Check 792

Divisible by 2 (ends in 2). Sum of digits is $7+9+2 = 18$, which is divisible by 3. Not divisible by 5 or 10 (ends in 2).

11. Check 854

Divisible by 2 (ends in 4). Sum of digits is $8+5+4 = 17$, which is NOT divisible by 3. Not divisible by 5 or 10 (ends in 4).

12. Check 904

Divisible by 2 (ends in 4). Sum of digits is $9+0+4 = 13$, which is NOT divisible by 3. Not divisible by 5 or 10 (ends in 4).

13. Final Answer

From the checks above, 360 is the only element of the set divisible by 2, 3, 5, and 10.