What is the greatest common factor of 18 and 50
The correct answer and explanation is:
The greatest common factor (GCF) of 18 and 50 is 2.
To find the greatest common factor, first list the factors of each number. Factors of a number are whole numbers that can be multiplied in pairs to produce that number.
Factors of 18 are 1, 2, 3, 6, 9, and 18.
Factors of 50 are 1, 2, 5, 10, 25, and 50.
Next, identify the common factors between the two lists. The common factors of 18 and 50 are 1 and 2.
Out of these common factors, the greatest one is 2.
The greatest common factor is useful for simplifying fractions, finding common denominators, and solving problems that involve dividing things into equal groups.
Another way to find the greatest common factor is to use the prime factorization method. Prime factorization breaks down each number into a product of prime numbers.
Prime factorization of 18 is 2 × 3 × 3.
Prime factorization of 50 is 2 × 5 × 5.
Then, find the common prime factors. Both numbers have a single 2 in their prime factorization.
Multiply the common prime factors to get the GCF. Here, it is just 2.
In conclusion, the greatest common factor of 18 and 50 is 2, found by identifying the highest factor that divides both numbers exactly. This helps in many areas of math such as simplifying fractions and solving problems involving grouping.