Ravi's teacher writes this challenge on the board: "Find a number that is both a factor of 84 and a multiple of 7." Which of the following numbers satisfies BOTH conditions?
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Worked Solution
Step 1: Understand the two conditions.
Condition A: the number must be a factor of 84 (84 ÷ number = whole number, no remainder).
Condition B: the number must be a multiple of 7 (number = 7 × whole number).
Step 2: List factors of 84.
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Step 3: From the factors of 84, identify which are also multiples of 7.
7 = 7 × 1 ✓
14 = 7 × 2 ✓
21 = 7 × 3 ✓
28 = 7 × 4 ✓
42 = 7 × 6 ✓
Step 4: Check which of the answer options appears in the list above.
21 is in the list → 21 is a factor of 84 AND a multiple of 7.
The answer is 21.
Correct answer: 21
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