How do you explain GCF in mathematics?
GCF or greatest common factor of two or more numbers is defined as largest possible number or integer which is the factor of all given number or in other words we can say that largest possible common number which completely divides the given numbers. GCF of two numbers can be represented as GCF (224, 280).
Properties of GCF
- The GCF of two or more given numbers cannot be greater than any of the given number. Eg- GCF of 224 and 280 is 56, where 56 is less than both 224 and 280.
- 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.
How can we define factors?
In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.
Properties of Factors
- Each number is a factor of itself. Eg. 224 and 280 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 224 and also of 280.
- Every number is a factor of zero (0), since 224 x 0 = 0 and 280 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, 7, 8, 14, 16, 28, 32, 56, 112, 224 are exact divisors of 224 and 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280 are exact divisors of 280.
- Factors of 224 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224. Each factor divides 224 without leaving a remainder.
Simlarly, factors of 280 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280. Each factor divides 280 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224 are all less than or equal to 224 and 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280 are all less than or equal to 280.
Steps to find Factors of 224 and 280
- Step 1. Find all the numbers that would divide 224 and 280 without leaving any remainder. Starting with the number 1 upto 112 (half of 224) and 1 upto 140 (half of 280). The number 1 and the number itself are always factors of the given number.
224 ÷ 1 : Remainder = 0
280 ÷ 1 : Remainder = 0
224 ÷ 2 : Remainder = 0
280 ÷ 2 : Remainder = 0
224 ÷ 4 : Remainder = 0
280 ÷ 4 : Remainder = 0
224 ÷ 7 : Remainder = 0
280 ÷ 5 : Remainder = 0
224 ÷ 8 : Remainder = 0
280 ÷ 7 : Remainder = 0
224 ÷ 14 : Remainder = 0
280 ÷ 8 : Remainder = 0
224 ÷ 16 : Remainder = 0
280 ÷ 10 : Remainder = 0
224 ÷ 28 : Remainder = 0
280 ÷ 14 : Remainder = 0
224 ÷ 32 : Remainder = 0
280 ÷ 20 : Remainder = 0
224 ÷ 56 : Remainder = 0
280 ÷ 28 : Remainder = 0
224 ÷ 112 : Remainder = 0
280 ÷ 35 : Remainder = 0
224 ÷ 224 : Remainder = 0
280 ÷ 40 : Remainder = 0
280 ÷ 140 : Remainder = 0
280 ÷ 280 : Remainder = 0
Hence, Factors of
224 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, and 224
And, Factors of
280 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, and 280
Examples of GCF
Sammy baked 224 chocolate cookies and 280 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 224 and 280.
GCF of 224 and 280 is 56.
A class has 224 boys and 280 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 224 and 280. Hence, GCF of 224 and 280 is 56.
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(224, 280) = ( 224 * 280 ) / LCM(224, 280) = 56.
What is the GCF of 224 and 280?GCF of 224 and 280 is 56.
Ariel is making ready to eat meals to share with friends. She has 224 bottles of water and 280 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 224 and 280. So the GCF of 224 and 280 is 56.
Mary has 224 blue buttons and 280 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 224 and 280. Hence, the GCF of 224 and 280 or the greatest arrangement is 56.
Kamal is making identical balloon arrangements for a party. He has 224 maroon balloons, and 280 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 224 and 280. So the GCF of 224 and 280 is 56.
Kunal is making baskets full of nuts and dried fruits. He has 224 bags of nuts and 280 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 224 and 280. So the GCF of 224 and 280 is 56.
A class has 224 boys and 280 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 224 and 280. Hence, GCF of 224 and 280 is 56.