Identify Number Not a Multiple of 3
To determine if a number is a multiple of 3, we can use the divisibility rule for 3. This rule states that a number is divisible by 3 if the sum of its digits is divisible by 3.
Checking Multiples of 3
Let's apply this rule to each of the given numbers:
-
Number: 369
Sum of digits: $3 + 6 + 9 = 18$
Check: $18 \div 3 = 6$. Since 18 is divisible by 3, 369 is a multiple of 3. -
Number: 372
Sum of digits: $3 + 7 + 2 = 12$
Check: $12 \div 3 = 4$. Since 12 is divisible by 3, 372 is a multiple of 3. -
Number: 375
Sum of digits: $3 + 7 + 5 = 15$
Check: $15 \div 3 = 5$. Since 15 is divisible by 3, 375 is a multiple of 3. -
Number: 377
Sum of digits: $3 + 7 + 7 = 17$
Check: $17 \div 3 \approx 5.67$. Since 17 is not divisible by 3, 377 is NOT a multiple of 3.
Conclusion
Based on the divisibility rule for 3, the number 377 is the only number among the options whose sum of digits (17) is not divisible by 3. Therefore, 377 is NOT a multiple of 3.
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Consider all 3-digit numbers (without repetition of digits) obtained using three non-zero digits which are multiples of 3. Let S be their sum.
Which of the following is/are correct?
1. S is always divisible by 74.
2. S is always divisible by 9.
select the correct answer using the code given below:
