what are the composite factors of 56
What are the composite factors of 56?
Answer:
To determine the composite factors of 56, it’s helpful to first revisit what composite numbers are. A composite number is a positive integer greater than one that is not prime, meaning it has more than two distinct positive divisors. In simpler terms, a composite number can be divided evenly by numbers other than 1 and itself.
Let’s find all the factors of 56 and identify which of them are composite.
Step 1: List All Factors of 56
A factor is a number that divides another number completely without leaving a remainder. To find the factors of 56, we identify all numbers less than or equal to 56 that divide 56 exactly:
- ( 1 \times 56 = 56 )
- ( 2 \times 28 = 56 )
- ( 4 \times 14 = 56 )
- ( 7 \times 8 = 56 )
Therefore, the factors of 56 are ( 1, 2, 4, 7, 8, 14, 28, ) and ( 56 ).
Step 2: Identify Composite Factors
Next, we need to determine which of these factors are composite numbers. From the list of factors, identify which ones are not prime:
- 1: Not composite or prime.
- 2: Prime (only divisible by 1 and 2).
- 4: Composite (divisible by 1, 2, and 4).
- 7: Prime (only divisible by 1 and 7).
- 8: Composite (divisible by 1, 2, 4, and 8).
- 14: Composite (divisible by 1, 2, 7, and 14).
- 28: Composite (divisible by 1, 2, 4, 7, 14, and 28).
- 56: Composite (divisible by 1, 2, 4, 7, 8, 14, 28, and 56).
Conclusion
The composite factors of 56 are 4, 8, 14, 28, and 56. These numbers have more than two divisors, meeting the definition of composite numbers.