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). Applying this rule to the list:

   • 360, 564, 792, 854, and 904 are divisible by 2.
   • 235, 487, and 681 are not divisible by 2.

2. Divisibility rule for 3: A number is divisible by 3 if the sum of its digits is divisible by 3. Applying this rule to the list:

   • For 235: $2 + 3 + 5 = 10$, which is not divisible by 3.
   • For 360: $3 + 6 + 0 = 9 $, which is divisible by 3.
   • For 487: $4 + 8 + 7 = 19$, which is not divisible by 3.
   • For 564: $5 + 6 + 4 = 15$, which is divisible by 3.
   • For 681: $6 + 8 + 1 = 15$, which is divisible by 3.
   • For 792: $7 + 9 + 2 = 18$, which is divisible by 3.
   • For 854: $8 + 5 + 4 = 17$, which is not divisible by 3.
   • For 904: $9 + 0 + 4 = 13$, which is not divisible by 3. So, 360, 564, 681, and 792 are divisible by 3.

3. Divisibility rule for 5: A number is divisible by 5 if its last digit is either 0 or 5. Applying this rule to the list:

   • 235 and 360 are divisible by 5. -The reset of them are not divisible by 5.

4. Divisibility rule for 10: A number is divisible by 10 if its last digit is 0. Among the initial list, only 360 is divisible by 10.

5. Find the numbers that satisfy all conditions: We need to find numbers that are divisible by 2, 3, 5, and 10.

From step 1, the numbers divisible by 2 are: 360, 564, 792, 854, and 904. From step 2, the numbers divisible by 3 are: 360, 564, 681, and 792. From step 3, the numbers divisible by 5 are: 235 and 360. From step 4, the numbers divisible by 10 are: 360.

The only number that satisfies all four conditions (divisible by 2, 3, 5, and 10) is 360.