Solved on Jan 24, 2024
Identify all composite numbers among 44, 28, and 37.
STEP 1
Assumptions
1. A composite number is a positive integer greater than 1 that has at least one positive divisor other than 1 and itself.
2. The numbers to be checked are 44, 28, and 37.
STEP 2
We will check each number to see if it has divisors other than 1 and itself.
STEP 3
First, we will check if 44 is a composite number.
STEP 4
We can quickly identify that 44 is an even number, which means it is divisible by 2.
STEP 5
Since 44 is divisible by 2, it has at least one divisor other than 1 and itself. Thus, 44 is a composite number.
STEP 6
Next, we will check if 28 is a composite number.
STEP 7
We can quickly identify that 28 is an even number, which means it is divisible by 2.
STEP 8
Since 28 is divisible by 2, it has at least one divisor other than 1 and itself. Thus, 28 is a composite number.
STEP 9
Finally, we will check if 37 is a composite number.
STEP 10
We observe that 37 is not an even number, so it is not divisible by 2.
STEP 11
We can check for divisibility by primes less than the square root of 37 to see if it has any divisors other than 1 and itself. The square root of 37 is approximately 6.08, so we only need to check for divisibility by primes less than or equal to 5, which are 2, 3, and 5.
STEP 12
We have already established that 37 is not divisible by 2 since it is not an even number.
STEP 13
Next, we check if 37 is divisible by 3. We can sum the digits of 37 (3 + 7 = 10) and see that the sum is not divisible by 3, so 37 is not divisible by 3.
STEP 14
Finally, we check if 37 is divisible by 5. Since 37 does not end in 0 or 5, it is not divisible by 5.
STEP 15
Since 37 has no divisors other than 1 and itself, it is not a composite number; it is a prime number.
The composite numbers from the list are 44 and 28.
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