Select the INCORRECT statement .

Options

A. The greatest number that exactly divides 63 and 84 is 21.
B. A factor of a number is an exact divisor of that number .
C. The smallest number that is exactly divisible by 12 , 14 , 18 , 22 is 2.
D. A number divisible by two co-prime numbers is divisible by their product also .

Answer

To solve the question of selecting the INCORRECT statement, we will analyze each option provided in the question step by step.

### Step 1: Analyze Option 1
**Statement**: The greatest number that exactly divides 63 and 84 is 21.

- To verify this, we need to find the Highest Common Factor (HCF) of 63 and 84.
- The factors of 63 are: 1, 3, 7, 9, 21, 63.
- The factors of 84 are: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.
- The common factors of 63 and 84 are: 1, 3, 7, 21.
- The greatest of these common factors is 21.

**Conclusion**: This statement is correct.

### Step 2: Analyze Option 2
**Statement**: A factor of a number is an exact divisor of that number.

- By definition, a factor is a number that divides another number without leaving a remainder.
- For example, 3 is a factor of 63 because 63 ÷ 3 = 21 with no remainder.

**Conclusion**: This statement is correct.

### Step 3: Analyze Option 3
**Statement**: The smallest number that is exactly divisible by 12, 14, 18, and 22 is 2.

- To verify this, we need to find the Least Common Multiple (LCM) of 12, 14, 18, and 22.
- The prime factorization is:
- 12 = 2² × 3
- 14 = 2 × 7
- 18 = 2 × 3²
- 22 = 2 × 11
- The LCM is found by taking the highest power of each prime:
- LCM = 2² × 3² × 7 × 11
- Calculating this gives us a number much larger than 2.

**Conclusion**: This statement is incorrect.

### Step 4: Analyze Option 4
**Statement**: A number divisible by two co-prime numbers is divisible by their product also.

- Co-prime numbers are numbers that have no common factors other than 1.
- For example, 7 and 11 are co-prime.
- If a number is divisible by both 7 and 11, it must also be divisible by 7 × 11 = 77.

**Conclusion**: This statement is correct.

### Final Conclusion
The INCORRECT statement is Option 3: "The smallest number that is exactly divisible by 12, 14, 18, and 22 is 2."

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