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Fill in the blanks. (i) The H.C.F. of ...

Fill in the blanks.
(i) The H.C.F. of two co-prime numbers is `ul(P)`
(ii) Two natural numbers which have no common factor except 1 are called `ul(Q)` numbers.
(iii) If a number is divisible by 9, then sum of its digits must be divisible by `ul(R)`

A

`{:("P Q R"),("1 prime 3 "):}`

B

`{:("P Q R"),("1 co-prime 9 "):}`

C

`{:("P Q R"),("0 prime 9 "):}`

D

`{:("P Q R"),("0 co- prime 9 "):}`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to fill in the blanks with the correct terms based on the definitions and properties of numbers. Let's go through each part step by step. ### Step 1: Identify the H.C.F. of Two Co-prime Numbers - Co-prime numbers are defined as two natural numbers that have no common factors other than 1. - Therefore, the highest common factor (H.C.F.) of two co-prime numbers is always **1**. **Fill in the blank (i):** The H.C.F. of two co-prime numbers is **1**. ### Step 2: Define Two Natural Numbers with No Common Factor Except 1 - Two natural numbers that have no common factors except for 1 are called **co-prime numbers**. - This means that if two numbers are co-prime, they do not share any factors other than 1. **Fill in the blank (ii):** Two natural numbers which have no common factor except 1 are called **co-prime** numbers. ### Step 3: Understand the Divisibility Rule for 9 - The rule states that if a number is divisible by 9, then the sum of its digits must also be divisible by **9**. - This is a specific property related to the number 9. **Fill in the blank (iii):** If a number is divisible by 9, then the sum of its digits must be divisible by **9**. ### Final Answers - (i) 1 - (ii) co-prime - (iii) 9 ---
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