Introduction to greatest prime factor:
In this section we will study about greatest prime factor. Greatest prime factor is also called as greatest common factor. It is used us to calculate the greatest prime factors of two or more numbers. In this section we will see some solved problems for greatest common factor. Let us study greatest prime factor.
Example Problems for Greatest Prime Factor:
Example problem 1: What is the greatest common factor of 4 and 2?
Solution:
First we have to write the prime factorization for 4 and 2. 2 is a prime number.
4 = 2 × 2
Next, find the common factors shared by both of the numbers.
4 = 2 × 2
2 = 2
The only common factor of 4 and 2 is 2, so the greatest common factor is 2.
Answer: The greatest common factor is 2.
Example problem 2: Dante has 12 math books and 18 science books. If he wants to distribute them evenly among some bookshelves so that each bookshelf has the same combination of math and science books, with no books left over, what is the greatest number of bookshelves Dante can use?
Solution:
Write the prime factorization for 12 and 18.
12 = 2 × 2 × 3
18 = 2 × 3 × 3
Next, find the common factors shared by both of the numbers.
12 = 2 × 2 × 3
18 = 2 × 3 × 3
Finally, multiply the common factors to find the greatest common factor.
2 × 3 = 6
The greatest common factor of 12 and 18 is 6. That means that the greatest possible number of bookshelves is 6, because 12 math books could be put onto 6 bookshelves with 2 math books each and 18 science books could be put onto 6 bookshelves with 3 science books each.
The greatest number of bookshelves Dante can use is 6.
Answer: The greatest number of bookshelves Dante can use is 6.
Practice Problems for Greatest Prime Factor:
Practice problem 1: Zahra and Raul are training for a marathon. Zahra runs 9 miles at a time while Raul prefers to run in blocks of 8 miles. At the end of a month, they realize that they have run same total number of miles. What is the smallest number of miles that each must have run?
Practice problem 2: The city of Hillsdale is honoring 15 mothers and 20 fathers as winners of its "Best Parent" contest. The plan is to take several group photographs, each with the same combination of mothers and fathers and no parents left out. What is the greatest number of photos that can be taken?
Solutions for greatest prime factor:
Solution 1: Each of them must have run 72 miles.
Solution 2: The greatest number of photos that can be taken is 5.
In this section we will study about greatest prime factor. Greatest prime factor is also called as greatest common factor. It is used us to calculate the greatest prime factors of two or more numbers. In this section we will see some solved problems for greatest common factor. Let us study greatest prime factor.
Example Problems for Greatest Prime Factor:
Example problem 1: What is the greatest common factor of 4 and 2?
Solution:
First we have to write the prime factorization for 4 and 2. 2 is a prime number.
4 = 2 × 2
Next, find the common factors shared by both of the numbers.
4 = 2 × 2
2 = 2
The only common factor of 4 and 2 is 2, so the greatest common factor is 2.
Answer: The greatest common factor is 2.
Example problem 2: Dante has 12 math books and 18 science books. If he wants to distribute them evenly among some bookshelves so that each bookshelf has the same combination of math and science books, with no books left over, what is the greatest number of bookshelves Dante can use?
Solution:
Write the prime factorization for 12 and 18.
12 = 2 × 2 × 3
18 = 2 × 3 × 3
Next, find the common factors shared by both of the numbers.
12 = 2 × 2 × 3
18 = 2 × 3 × 3
Finally, multiply the common factors to find the greatest common factor.
2 × 3 = 6
The greatest common factor of 12 and 18 is 6. That means that the greatest possible number of bookshelves is 6, because 12 math books could be put onto 6 bookshelves with 2 math books each and 18 science books could be put onto 6 bookshelves with 3 science books each.
The greatest number of bookshelves Dante can use is 6.
Answer: The greatest number of bookshelves Dante can use is 6.
Practice Problems for Greatest Prime Factor:
Practice problem 1: Zahra and Raul are training for a marathon. Zahra runs 9 miles at a time while Raul prefers to run in blocks of 8 miles. At the end of a month, they realize that they have run same total number of miles. What is the smallest number of miles that each must have run?
Practice problem 2: The city of Hillsdale is honoring 15 mothers and 20 fathers as winners of its "Best Parent" contest. The plan is to take several group photographs, each with the same combination of mothers and fathers and no parents left out. What is the greatest number of photos that can be taken?
Solutions for greatest prime factor:
Solution 1: Each of them must have run 72 miles.
Solution 2: The greatest number of photos that can be taken is 5.
