Question

If in the division algorithm \(a=bq+r\), \(a=72\), \(q=8\) and \(r=0\), then what is the value of \(b\)?

• A. \(9\)
• B. \(8\)
• C. \(7\)
• D. \(4\)

Hint:

When the remainder \(r=0\), the dividend is exactly divisible: \(a=bq\), so \(b=\dfrac{a}{q}\).

Answer 1

The Correct Option is A

Step 1: Recall the division algorithm.
It states \(a=bq+r\) with \(0 \le r<b\). Here \(r=0\), so \(a=bq\).
Step 2: Substitute the given values and solve for \(b\).
\(72 = b \cdot 8 \Rightarrow b = \dfrac{72}{8} = 9.\)
Step 3: Conclude.
Therefore, \(b=9\).