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 (220, 2924).
Properties of GCF
- The GCF of two or more given numbers cannot be greater than any of the given number. Eg- GCF of 220 and 2924 is 4, where 4 is less than both 220 and 2924.
- 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. 220 and 2924 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 220 and also of 2924.
- Every number is a factor of zero (0), since 220 x 0 = 0 and 2924 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, 10, 11, 20, 22, 44, 55, 110, 220 are exact divisors of 220 and 1, 2, 4, 17, 34, 43, 68, 86, 172, 731, 1462, 2924 are exact divisors of 2924.
- Factors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220. Each factor divides 220 without leaving a remainder.
Simlarly, factors of 2924 are 1, 2, 4, 17, 34, 43, 68, 86, 172, 731, 1462, 2924. Each factor divides 2924 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220 are all less than or equal to 220 and 1, 2, 4, 17, 34, 43, 68, 86, 172, 731, 1462, 2924 are all less than or equal to 2924.
Steps to find Factors of 220 and 2924
- Step 1. Find all the numbers that would divide 220 and 2924 without leaving any remainder. Starting with the number 1 upto 110 (half of 220) and 1 upto 1462 (half of 2924). The number 1 and the number itself are always factors of the given number.
220 ÷ 1 : Remainder = 0
2924 ÷ 1 : Remainder = 0
220 ÷ 2 : Remainder = 0
2924 ÷ 2 : Remainder = 0
220 ÷ 4 : Remainder = 0
2924 ÷ 4 : Remainder = 0
220 ÷ 5 : Remainder = 0
2924 ÷ 17 : Remainder = 0
220 ÷ 10 : Remainder = 0
2924 ÷ 34 : Remainder = 0
220 ÷ 11 : Remainder = 0
2924 ÷ 43 : Remainder = 0
220 ÷ 20 : Remainder = 0
2924 ÷ 68 : Remainder = 0
220 ÷ 22 : Remainder = 0
2924 ÷ 86 : Remainder = 0
220 ÷ 44 : Remainder = 0
2924 ÷ 172 : Remainder = 0
220 ÷ 55 : Remainder = 0
2924 ÷ 731 : Remainder = 0
220 ÷ 110 : Remainder = 0
2924 ÷ 1462 : Remainder = 0
220 ÷ 220 : Remainder = 0
2924 ÷ 2924 : Remainder = 0
Hence, Factors of
220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, and 220
And, Factors of
2924 are 1, 2, 4, 17, 34, 43, 68, 86, 172, 731, 1462, and 2924
Examples of GCF
Sammy baked 220 chocolate cookies and 2924 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 220 and 2924.
GCF of 220 and 2924 is 4.
A class has 220 boys and 2924 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 220 and 2924. Hence, GCF of 220 and 2924 is 4.
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(220, 2924) = ( 220 * 2924 ) / LCM(220, 2924) = 4.
What is the GCF of 220 and 2924?GCF of 220 and 2924 is 4.
Mary has 220 blue buttons and 2924 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 220 and 2924. Hence, the GCF of 220 and 2924 or the greatest arrangement is 4.
Kamal is making identical balloon arrangements for a party. He has 220 maroon balloons, and 2924 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 220 and 2924. So the GCF of 220 and 2924 is 4.
Kunal is making baskets full of nuts and dried fruits. He has 220 bags of nuts and 2924 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 220 and 2924. So the GCF of 220 and 2924 is 4.
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 220 bus tickets and 2924 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 220 and 2924. Hence, GCF of 220 and 2924 is 4.