What are factor pairs for the number 51?
The Correct Answer and Explanation is:
Factor Pairs of 51:
The factor pairs of 51 are:
- 1 × 51
- 3 × 17
So, the factor pairs of 51 are (1, 51) and (3, 17).
Explanation:
A factor pair of a number consists of two whole numbers that, when multiplied together, give the original number. In this case, we’re finding factor pairs of 51, which means we’re identifying all the combinations of two whole numbers whose product is 51.
To find factor pairs of 51, we start by dividing 51 by small whole numbers, beginning with 1.
- 1 × 51 = 51, so (1, 51) is a factor pair.
- Next, try 2. Since 51 is an odd number, it is not divisible by 2.
- Try 3. 51 ÷ 3 = 17, and 17 is a whole number, so (3, 17) is a valid factor pair.
- Next, try 4. 51 ÷ 4 = 12.75, which is not a whole number.
- Continue trying whole numbers up to the square root of 51 (approximately 7.14). We do this because factor pairs repeat after the square root (e.g., if 3 × 17 is a pair, then 17 × 3 is just the same pair reversed).
Beyond 7, the other numbers either don’t divide evenly into 51 or simply reverse the earlier factor pairs.
The number 51 is not a prime number, because it has more than two factors (1, 3, 17, and 51). But it is not highly composite either, as it has only four factors.
Understanding factor pairs is important in many areas of math such as simplifying fractions, finding least common multiples, or solving problems involving area and perimeter. In algebra, factor pairs also help in factoring expressions or solving quadratic equations.
So, the correct and complete factor pairs of 51 are:
- (1, 51)
- (3, 17)
These represent all possible positive factor combinations for 51.
