Entre los siguientes números, encuentre los que son múltiplos de 2, 3, 5 y 10: 235, 360, 487, 564, 681, 792, 854, 904.
Understand the Problem
La pregunta pide identificar, de entre una lista de números dados, cuáles son múltiplos de 2, 3, 5 y 10. Para resolverlo, hay que verificar la divisibilidad de cada número de la lista entre estos cuatro valores.
Answer
Multiples of 2: $360, 564, 792, 854, 904$ Multiples of 3: $360, 564, 681, 792$ Multiples of 5: $235, 360$ Multiples of 10: $360$
Answer for screen readers
Multiples of 2: $360, 564, 792, 854, 904$
Multiples of 3: $360, 564, 681, 792$
Multiples of 5: $235, 360$
Multiples of 10: $360$
Steps to Solve
- Divisibility by 2
A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8). We check each number:
235: Last digit is 5 (odd). Not divisible by 2.
360: Last digit is 0 (even). Divisible by 2.
487: Last digit is 7 (odd). Not divisible by 2.
564: Last digit is 4 (even). Divisible by 2.
681: Last digit is 1 (odd). Not divisible by 2.
792: Last digit is 2 (even). Divisible by 2.
854: Last digit is 4 (even). Divisible by 2.
904: Last digit is 4 (even). Divisible by 2.
- Divisibility by 3
A number is divisible by 3 if the sum of its digits is divisible by 3.
235: $2 + 3 + 5 = 10$. 10 is not divisible by 3.
360: $3 + 6 + 0 = 9$. 9 is divisible by 3.
487: $4 + 8 + 7 = 19$. 19 is not divisible by 3.
564: $5 + 6 + 4 = 15$. 15 is divisible by 3.
681: $6 + 8 + 1 = 15$. 15 is divisible by 3.
792: $7 + 9 + 2 = 18$. 18 is divisible by 3.
854: $8 + 5 + 4 = 17$. 17 is not divisible by 3.
904: $9 + 0 + 4 = 13$. 13 is not divisible by 3.
- Divisibility by 5
A number is divisible by 5 if its last digit is 0 or 5.
235: Last digit is 5. Divisible by 5.
360: Last digit is 0. Divisible by 5.
487: Last digit is 7. Not divisible by 5.
564: Last digit is 4. Not divisible by 5.
681: Last digit is 1. Not divisible by 5.
792: Last digit is 2. Not divisible by 5.
854: Last digit is 4. Not divisible by 5.
904: Last digit is 4. Not divisible by 5.
- Divisibility by 10
A number is divisible by 10 if its last digit is 0.
235: Last digit is 5. Not divisible by 10.
360: Last digit is 0. Divisible by 10.
487: Last digit is 7. Not divisible by 10.
564: Last digit is 4. Not divisible by 10.
681: Last digit is 1. Not divisible by 10.
792: Last digit is 2. Not divisible by 10.
854: Last digit is 4. Not divisible by 10.
904: Last digit is 4. Not divisible by 10.
- Final Results
Now we summarize which numbers are multiples of 2, 3, 5, and 10:
Multiples of 2: 360, 564, 792, 854, 904 Multiples of 3: 360, 564, 681, 792 Multiples of 5: 235, 360 Multiples of 10: 360
Multiples of 2: $360, 564, 792, 854, 904$
Multiples of 3: $360, 564, 681, 792$
Multiples of 5: $235, 360$
Multiples of 10: $360$
More Information
A number divisible by 10 must end in 0, therefore it is also always divisible by both 2 and 5.
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