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 (40, 120).
Properties of GCF
- The GCF of two or more given numbers cannot be greater than any of the given number. Eg- GCF of 40 and 120 is 40, where 40 is less than both 40 and 120.
- GCF of two consecutive numbers is always 1.
- The product of GCF and LCM of two given numbers is equal to the product of two numbers.
- 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
- Each number is a factor of itself. Eg. 40 and 120 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 40 and also of 120.
- Every number is a factor of zero (0), since 40 x 0 = 0 and 120 x 0 = 0.
- Every number other than 1 has at least two factors, namely the number itself and 1.
- Every factor of a number is an exact divisor of that number, example 1, 2, 4, 5, 8, 10, 20, 40 are exact divisors of 40 and 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 are exact divisors of 120.
- Factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40. Each factor divides 40 without leaving a remainder.
Simlarly, factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. Each factor divides 120 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 5, 8, 10, 20, 40 are all less than or equal to 40 and 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 are all less than or equal to 120.
Steps to find Factors of 40 and 120
- Step 1. Find all the numbers that would divide 40 and 120 without leaving any remainder. Starting with the number 1 upto 20 (half of 40) and 1 upto 60 (half of 120). The number 1 and the number itself are always factors of the given number.
40 ÷ 1 : Remainder = 0
120 ÷ 1 : Remainder = 0
40 ÷ 2 : Remainder = 0
120 ÷ 2 : Remainder = 0
40 ÷ 4 : Remainder = 0
120 ÷ 3 : Remainder = 0
40 ÷ 5 : Remainder = 0
120 ÷ 4 : Remainder = 0
40 ÷ 8 : Remainder = 0
120 ÷ 5 : Remainder = 0
40 ÷ 10 : Remainder = 0
120 ÷ 6 : Remainder = 0
40 ÷ 20 : Remainder = 0
120 ÷ 8 : Remainder = 0
40 ÷ 40 : Remainder = 0
120 ÷ 10 : Remainder = 0
120 ÷ 120 : Remainder = 0
Hence, Factors of
40 are 1, 2, 4, 5, 8, 10, 20, and 40
And, Factors of
120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120
Examples of GCF
Sammy baked 40 chocolate cookies and 120 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 40 and 120.
GCF of 40 and 120 is 40.
A class has 40 boys and 120 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 40 and 120. Hence, GCF of 40 and 120 is 40.
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(40, 120) = ( 40 * 120 ) / LCM(40, 120) = 40.
What is the GCF of 40 and 120?GCF of 40 and 120 is 40.
Mary has 40 blue buttons and 120 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 40 and 120. Hence, the GCF of 40 and 120 or the greatest arrangement is 40.
Kamal is making identical balloon arrangements for a party. He has 40 maroon balloons, and 120 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 40 and 120. So the GCF of 40 and 120 is 40.
Kunal is making baskets full of nuts and dried fruits. He has 40 bags of nuts and 120 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 40 and 120. So the GCF of 40 and 120 is 40.
To energize public transportation, Abir needs to give a few companions envelopes with transport tickets, and metro tickets in them. On the off chance that he has 40 bus tickets and 120 metro tickets to be parted similarly among the envelopes, and he need no tickets left. What is the greatest number of envelopes Abir can make?To make the greatest number of envelopes Abir needs to find out the GCF of 40 and 120. Hence, GCF of 40 and 120 is 40.