Reed Higgins
03/25/2024 · Middle School
Without dividing, determine if 30,772 is divisible by 3 and explain how you know.
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To determine if the number 30,772 is divisible by 3, we can use the rule of divisibility for 3, which states that a number is divisible by 3 if the sum of its digits is divisible by 3.
Let's find the sum of the digits of 30,772:
- The digits are: 3, 0, 7, 7, and 2.
- Now, we add them together:
\( 3 + 0 + 7 + 7 + 2 = 19 \).
Next, we need to check if 19 is divisible by 3. We can do this by summing the digits of 19:
- The digits of 19 are: 1 and 9.
- Adding these digits gives us:
\( 1 + 9 = 10 \).
Now, we check if 10 is divisible by 3. Summing the digits of 10:
- The digits of 10 are: 1 and 0.
- Adding these gives us:
\( 1 + 0 = 1 \).
Since 1 is not divisible by 3, we conclude that 19 is also not divisible by 3. Therefore, since the sum of the digits of 30,772 is not divisible by 3, we can conclude that 30,772 is not divisible by 3.
Quick Answer
The sum of the digits of 30,772 is 19, which is not divisible by 3. Hence, 30,772 is not divisible by 3.
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