Answer :
Let's find Igor's number following these steps:
1. Identify the common divisors of 54 and 24.
2. From the common divisors, find those that are odd.
3. Among the odd divisors, choose the one which is greater than 2.
**Step 1: Find common divisors**
First, let's factorize 54 and 24 to find their common factors.
The prime factorization of 54 is:
54 = 2 x 3 x 3 x 3
54 = 2 x 3^3
The prime factorization of 24 is:
24 = 2 x 2 x 2 x 3
24 = 2^3 x 3
Both numbers share the common factors 2 and 3. Since we are interested in divisors that are shared by both numbers, we will consider only the powers of these primes that appear in both factorizations. In this case, the highest power of 2 common in both is simply 2^1 (since 24 has 2^3 and 54 has 2^1, the minimum is 2^1), and the highest power of 3 common in both is 3^1 (since 54 has 3^3 and 24 has 3^1, the minimum is 3^1).
Therefore, the greatest common divisor (GCD) is:
GCD(54, 24) = 2^1 * 3^1
GCD(54, 24) = 2 * 3
GCD(54, 24) = 6
Now, let's list the divisors of 6 that are common to both 54 and 24:
1, 2, 3, 6
**Step 2: Identify odd divisors**
From the list above, we need to select the divisors that are odd. The odd numbers in the list are:
1, 3
**Step 3: Choose divisor greater than 2**
From the odd divisors, we need to find one that is greater than 2. The only odd divisor left that is greater than 2 is:
3
Therefore, Igor's number is 3, as it is the largest odd divisor greater than 2 that is a common divisor of both 54 and 24.
