what are the factor pairs for 24
The correct answer and explanation is:
The factor pairs of 24 are the combinations of whole numbers that, when multiplied together, equal 24. The process for finding factor pairs involves dividing 24 by all integers starting from 1, and pairing each divisor with the quotient to find all factor combinations.
The factor pairs of 24 are:
- (1, 24)
- (2, 12)
- (3, 8)
- (4, 6)
To explain this systematically:
- Start with the number 1. Since 24 ÷ 1 = 24, the pair is (1, 24).
- Move to the next integer, 2. Dividing 24 by 2 gives 12, so the pair is (2, 12).
- Next, check 3. Dividing 24 by 3 gives 8, so the pair is (3, 8).
- Next, try 4. Dividing 24 by 4 gives 6, so the pair is (4, 6).
- After 4, the next integer would be 5, but 24 ÷ 5 does not result in a whole number, so 5 is not a factor.
- Since factors above 4 will simply repeat the pairs in reverse (like (6, 4), (8, 3), etc.), the process stops here.
The total number of factor pairs for 24 is four: (1, 24), (2, 12), (3, 8), and (4, 6). These factor pairs show all the possible ways to break down the number 24 into two whole numbers whose product is 24.
Factor pairs are important in mathematics, particularly in problems involving divisibility, prime factorization, and simplifying fractions. They also help in understanding the structure of a number and in solving various algebraic equations and problems.