what is the greatest common factor of 15 and 25
The Correct Answer and Explanation is:
The greatest common factor (GCF) of 15 and 25 is 5.
To find the greatest common factor of two numbers, we look for the largest number that divides both numbers exactly, meaning it leaves no remainder.
Let’s begin by listing the factors of each number.
The factors of 15 are:
1, 3, 5, 15
The factors of 25 are:
1, 5, 25
Now, identify the common factors. These are the numbers that appear in both lists. The common factors of 15 and 25 are:
1 and 5
Out of these, the greatest one is 5. Therefore, the GCF of 15 and 25 is 5.
Another way to find the GCF is by using prime factorization.
The prime factorization of 15 is:
3 × 5
The prime factorization of 25 is:
5 × 5
Now, find the common prime factors. Both 15 and 25 have at least one 5 in their factorization. So the GCF is 5.
Understanding greatest common factors is important in simplifying fractions, solving problems in number theory, and reducing ratios to their simplest form. For example, if you had the fraction 15 over 25, you could simplify it by dividing both the numerator and the denominator by their GCF. Dividing both 15 and 25 by 5 gives 3 over 5, which is the simplified form of the fraction.
Knowing how to find the GCF also helps in solving real-world problems. Suppose you are organizing items into groups and you want to create the largest equal groups possible without leftovers. The GCF tells you the maximum size of each group. If you had 15 apples and 25 oranges and you wanted to make identical fruit baskets with no leftover fruit, each basket could contain 5 apples or oranges. This is because 5 is the largest number that evenly divides both 15 and 25.
