Finding the HCF of Smallest Prime and Smallest Compound Number

To find the HCF (Highest Common Factor) of the smallest prime number and the smallest compound number, we first need to identify these two numbers.

Understanding Prime and Compound Numbers

• Prime Number: A natural number greater than 1 that has no positive divisors other than 1 and itself. Examples: 2, 3, 5, 7, 11...
• Compound Number: A positive integer greater than 1 that is not prime. It has at least one divisor other than 1 and itself. Examples: 4, 6, 8, 9, 10...

Identifying the Smallest Numbers

• The smallest natural number is 1. It is neither prime nor compound.
• The next natural number is 2. Its only divisors are 1 and 2. So, 2 is the smallest prime number.
• The next natural number is 3. Its only divisors are 1 and 3. So, 3 is a prime number.
• The next natural number is 4. Its divisors are 1, 2, and 4. Since it has a divisor (2) other than 1 and itself, 4 is a compound number. It is the first compound number we encounter after 1, 2, and 3. Therefore, 4 is the smallest compound number.

So, we need to find the HCF of 2 (the smallest prime number) and 4 (the smallest compound number).

Calculating the HCF of 2 and 4

The HCF is the largest number that divides both numbers without leaving a remainder. We can find the HCF by listing the factors of each number.

• Factors of 2: The numbers that divide 2 exactly are 1 and 2.
• Factors of 4: The numbers that divide 4 exactly are 1, 2, and 4.

Now, let's identify the common factors, which are the numbers that appear in both lists:

• Common factors of 2 and 4 are 1 and 2.

The highest among these common factors is 2.

Therefore, the HCF of the smallest prime number (2) and the smallest compound number (4) is 2.