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 (154, 294).
Properties of GCF
- Given two numbers 154 and 294, such that GCF is 14 where 14 will always be less than 154 and 294.
- GCF of two numbers is always equal to 1 in case given numbers are consecutive.
- The product of GCF and LCM of two given numbers is equal to the product of two numbers.
- The GCF of two given numbers is either 1 or the number itself if one of them is a prime number.
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. 154 and 294 are factors of themselves respectively.
- 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, 7, 11, 14, 22, 77, 154 are exact divisors of 154 and 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294 are exact divisors of 294.
- 1 is a factor of every number. Eg. 1 is a factor of 154 and also of 294.
- Every number is a factor of zero (0), since 154 x 0 = 0 and 294 x 0 = 0.
Steps to find Factors of 154 and 294
- Step 1. Find all the numbers that would divide 154 and 294 without leaving any remainder. Starting with the number 1 upto 77 (half of 154) and 1 upto 147 (half of 294). The number 1 and the number itself are always factors of the given number.
154 ÷ 1 : Remainder = 0
294 ÷ 1 : Remainder = 0
154 ÷ 2 : Remainder = 0
294 ÷ 2 : Remainder = 0
154 ÷ 7 : Remainder = 0
294 ÷ 3 : Remainder = 0
154 ÷ 11 : Remainder = 0
294 ÷ 6 : Remainder = 0
154 ÷ 14 : Remainder = 0
294 ÷ 7 : Remainder = 0
154 ÷ 22 : Remainder = 0
294 ÷ 14 : Remainder = 0
154 ÷ 77 : Remainder = 0
294 ÷ 21 : Remainder = 0
154 ÷ 154 : Remainder = 0
294 ÷ 42 : Remainder = 0
294 ÷ 147 : Remainder = 0
294 ÷ 294 : Remainder = 0
Hence, Factors of
154 are 1, 2, 7, 11, 14, 22, 77, and 154
And, Factors of
294 are 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, and 294
Examples of GCF
Sammy baked 154 chocolate cookies and 294 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 154 and 294.
GCF of 154 and 294 is 14.
A class has 154 boys and 294 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 154 and 294. Hence, GCF of 154 and 294 is 14.
What is the relation between LCM and GCF (Greatest Common Factor)?GCF and LCM of two numbers can be related as GCF(154, 294) = ( 154 * 294 ) / LCM(154, 294) = 14.
What is the GCF of 154 and 294?GCF of 154 and 294 is 14.
Ram has 154 cans of Pepsi and 294 cans of Coca Cola. He wants to create identical refreshment tables that will be organized in his house warming party. He also doesn't want to have any can left over. What is the greatest number of tables that Ram can arrange?To find the greatest number of tables that Ram can stock we need to find the GCF of 154 and 294. Hence GCF of 154 and 294 is 14. So the number of tables that can be arranged is 14.
Mary has 154 blue buttons and 294 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 154 and 294. Hence, the GCF of 154 and 294 or the greatest arrangement is 14.
Kamal is making identical balloon arrangements for a party. He has 154 maroon balloons, and 294 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 154 and 294. So the GCF of 154 and 294 is 14.
Kunal is making baskets full of nuts and dried fruits. He has 154 bags of nuts and 294 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 154 and 294. So the GCF of 154 and 294 is 14.
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 154 bus tickets and 294 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 154 and 294. Hence, GCF of 154 and 294 is 14.