Question

What prime number is a factor of
36
,
28
36,28, and
40
40?

Answer 1

To find a prime number that is a factor of the numbers 36, 28, and 40, we can start by determining the prime factorizations of each number.

1. **Factorization of 36:**
\[
36 = 2^2 \times 3^2
\]
The prime factors of 36 are 2 and 3.

2. **Factorization of 28:**
\[
28 = 2^2 \times 7
\]
The prime factors of 28 are 2 and 7.

3. **Factorization of 40:**
\[
40 = 2^3 \times 5
\]
The prime factors of 40 are 2 and 5.

Now, we can see which prime factors are common among the three numbers:

- The prime factor **2** is present in all three factorizations (36, 28, and 40).
- The other prime factors (3, 7, and 5) do not appear in all three numbers.

Thus, the prime number that is a factor of 36, 28, and 40 is:

\[
\boxed{2}
\]