Let P = QQQ be a 3-digit number. What is the HCF of P and 481?
- A1
- B13
- C37Correct
- D481
Explanation
To solve this, we first express P based on its digits. Since P is QQQ, it can be written as 100Q + 10Q + Q, which equals 111 multiplied by Q.
Next, we factorize the two numbers:
- P = 111 multiplied by Q. The number 111 can be broken down into 3 multiplied by 37. So, P = 3 multiplied by 37 multiplied by Q.
- The number 481 can be factorized into 13 multiplied by 37.
To find the Highest Common Factor (HCF), we look for the common factors between P and 481. The number 37 is a factor of both 111 (and thus P) and 481.
While Q could theoretically be 13, in a 3-digit number QQQ, Q must be a single digit from 1 to 9. Therefore, Q cannot be 13. This means 13 is not a common factor.
The only certain common factor between P and 481 is 37. Thus, the HCF is 37.
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