What are the factors of 51?
The correct answer and explanation is:
Correct Answer:
The factors of 51 are 1, 3, 17, and 51.
Explanation:
A factor is a number that divides another number exactly without leaving a remainder. To find the factors of 51, begin by testing small whole numbers.
Start with 1. Any whole number is divisible by 1, so 1 is always a factor.
Next, check 2. Since 51 is an odd number, it is not divisible by 2.
Then try 3. Add the digits of 51: 5 + 1 = 6. Since 6 is divisible by 3, this means 51 is divisible by 3. Now divide 51 by 3:
51 ÷ 3 = 17. So, 3 and 17 are both factors.
Continue checking higher numbers. After 17, the next logical step is to try 51 ÷ 17. That equals 3, which has already been found. Finally, 51 is divisible by itself, so 51 is a factor.
Thus, the complete list of factors of 51 is 1, 3, 17, and 51.
These numbers are important in math because they help identify whether a number is prime or composite. A prime number has only two factors: 1 and itself. Since 51 has more than two factors, it is a composite number.
Factors also help in simplifying fractions, finding least common multiples (LCMs), and solving equations involving divisibility. For example, if asked to simplify the fraction 51/102, knowing the factors helps divide both the numerator and the denominator by 51 to get 1/2.
Understanding factors builds foundational skills in arithmetic, algebra, and number theory. It trains logical thinking and promotes step-by-step problem-solving. This is especially helpful in early math education and advanced topics like factoring polynomials or solving equations.