What number could go into 27 and 72? This question often arises when people are trying to find the common factors of these two numbers. In mathematics, finding the common factors of two numbers is a fundamental concept that helps in understanding their relationship and divisibility. In this article, we will explore the number that can divide both 27 and 72, and discuss the significance of this number in the context of these two numbers.
The number that can go into both 27 and 72 is 9. To understand why 9 is the common factor, we need to first find the prime factors of each number. Prime factors are the building blocks of a number, and they help us understand the number’s divisibility.
Let’s start with 27. The prime factors of 27 are 3 and 3, since 27 can be expressed as 3 multiplied by itself twice (3 x 3 x 3). Now, let’s move on to 72. The prime factors of 72 are 2, 2, 2, 3, and 3, as 72 can be expressed as 2 multiplied by itself three times and 3 multiplied by itself twice (2 x 2 x 2 x 3 x 3).
To find the common factors, we need to identify the prime factors that are present in both numbers. In this case, the common prime factors are 3 and 3. Since both numbers have two 3s as prime factors, the number that can go into both 27 and 72 is 9 (3 x 3).
The significance of this number lies in the fact that it helps us understand the relationship between 27 and 72. For instance, if we want to divide 27 by 9, we get 3, which is the quotient. Similarly, if we divide 72 by 9, we get 8, which is also the quotient. This shows that 9 is a common factor that divides both numbers evenly.
Moreover, the concept of common factors is crucial in various real-life applications, such as simplifying fractions, solving equations, and finding the greatest common divisor (GCD) of two numbers. In the case of 27 and 72, the GCD is 9, which means that 9 is the largest number that can divide both 27 and 72 without leaving a remainder.
In conclusion, the number that can go into both 27 and 72 is 9. This number is significant because it represents the common factors of the two numbers and helps us understand their relationship and divisibility. By exploring the prime factors of these numbers, we can see how the concept of common factors is essential in mathematics and its applications.
