Definition of GCF
Greatest common factor commonly known as GCF of the two numbers is the highest possible number which completely divides given numbers, i.e. without leaving any remainder. It is represented as GCF (25, 90).
Properties of GCF
- The GCF of two or more given numbers is always less than the given numbers. Eg- GCF of 25 and 90 is 5, where 5 is less than both the numbers.
- If the given numbers are consecutive than GCF is always 1.
- Product of two numbers is always equal to the product of their GCF and LCM.
- The GCF of two given numbers where one of them is a prime number is either 1 or the number itself.
What are factors?
In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.
Properties of Factors
- Every factor of a number is an exact divisor of that number, example 1, 5, 25 are exact divisors of 25 and 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 are exact divisors of 90.
- Every number other than 1 has at least two factors, namely the number itself and 1.
- Each number is a factor of itself. Eg. 25 and 90 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 25 and also of 90.
Steps to find Factors of 25 and 90
- Step 1. Find all the numbers that would divide 25 and 90 without leaving any remainder. Starting with the number 1 upto 12 (half of 25) and 1 upto 45 (half of 90). The number 1 and the number itself are always factors of the given number.
25 ÷ 1 : Remainder = 0
90 ÷ 1 : Remainder = 0
25 ÷ 5 : Remainder = 0
90 ÷ 2 : Remainder = 0
25 ÷ 25 : Remainder = 0
90 ÷ 3 : Remainder = 0
Hence, Factors of
25 are 1, 5, and 25
And, Factors of
90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90
Examples of GCF
Sammy baked 25 chocolate cookies and 90 fruit and nut cookies to package in plastic containers for her friends at college. She wants to divide the cookies into identical boxes so that each box has the same number of each kind of cookies. She wishes that each box should have greatest number of cookies possible, how many plastic boxes does she need?
Since Sammy wants to pack greatest number of cookies possible. So for calculating total number of boxes required we need to calculate the GCF of 25 and 90.
GCF of 25 and 90 is 5.
A class has 25 boys and 90 girls. A choir teacher wants to form a choir team from this class such that the students are standing in equal rows also girls or boys will be in each row. Teacher wants to know the greatest number of students that could be in each row, can you help him?
To find the greatest number of students that could be in each row, we need to find the GCF of 25 and 90. Hence, GCF of 25 and 90 is 5.
What is the difference between GCF and LCM?
Major and simple difference betwen GCF and LCM is that GCF gives you the greatest common factor while LCM finds out the least common factor possible for the given numbers.
What is the relation between LCM and GCF (Greatest Common Factor)?
GCF and LCM of two numbers can be related as GCF(25, 90) = ( 25 * 90 ) / LCM(25, 90) = 5.
What is the GCF of 25 and 90?
GCF of 25 and 90 is 5.
Ariel is making ready to eat meals to share with friends. She has 25 bottles of water and 90 cans of food, which she would like to distribute equally, with no left overs. What is the greatest number of boxes Ariel can make?
The greatest number of boxes Ariel can make would be equal to GCF of 25 and 90. So the GCF of 25 and 90 is 5.
Mary has 25 blue buttons and 90 white buttons. She wants to place them in identical groups without any buttons left, in the greatest way possible. Can you help Mary arranging them in groups?
Greatest possible way in which Mary can arrange them in groups would be GCF of 25 and 90. Hence, the GCF of 25 and 90 or the greatest arrangement is 5.
Kamal is making identical balloon arrangements for a party. He has 25 maroon balloons, and 90 orange balloons. He wants each arrangement tohave the same number of each color. What is the greatest number of arrangements that he can make if every balloon is used?
The greatest number of arrangements that he can make if every balloon is used would be equal to GCF of 25 and 90. So the GCF of 25 and 90 is 5.
Kunal is making baskets full of nuts and dried fruits. He has 25 bags of nuts and 90 bags of dried fruits. He wants each basket to be identical, containing the same combination of bags of nuts and bags of driesn fruits, with no left overs. What is the greatest number of baskets that Kunal can make?
the greatest number of baskets that Kunal can make would be equal to GCF of 25 and 90. So the GCF of 25 and 90 is 5.