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 (245, 294).
Properties of GCF
- The GCF of two or more given numbers is always less than the given numbers. Eg- GCF of 245 and 294 is 49, where 49 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, 7, 35, 49, 245 are exact divisors of 245 and 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294 are exact divisors of 294.
- Every number other than 1 has at least two factors, namely the number itself and 1.
- Each number is a factor of itself. Eg. 245 and 294 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 245 and also of 294.
Steps to find Factors of 245 and 294
- Step 1. Find all the numbers that would divide 245 and 294 without leaving any remainder. Starting with the number 1 upto 122 (half of 245) and 1 upto 147 (half of 294). The number 1 and the number itself are always factors of the given number.
245 ÷ 1 : Remainder = 0
294 ÷ 1 : Remainder = 0
245 ÷ 5 : Remainder = 0
294 ÷ 2 : Remainder = 0
245 ÷ 7 : Remainder = 0
294 ÷ 3 : Remainder = 0
245 ÷ 35 : Remainder = 0
294 ÷ 6 : Remainder = 0
245 ÷ 49 : Remainder = 0
294 ÷ 7 : Remainder = 0
245 ÷ 245 : Remainder = 0
294 ÷ 14 : Remainder = 0
294 ÷ 147 : Remainder = 0
294 ÷ 294 : Remainder = 0
Hence, Factors of
245 are 1, 5, 7, 35, 49, and 245
And, Factors of
294 are 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, and 294
Examples of GCF
A class has 245 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 245 and 294. Hence, GCF of 245 and 294 is 49.
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(245, 294) = ( 245 * 294 ) / LCM(245, 294) = 49.
What is the GCF of 245 and 294?GCF of 245 and 294 is 49.
Ram has 245 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 245 and 294. Hence GCF of 245 and 294 is 49. So the number of tables that can be arranged is 49.
Rubel is creating individual servings of starters for her birthday party. He has 245 pizzas and 294 hamburgers. He wants each serving to be identical, with no left overs. Can you help Rubel in arranging the same in greatest possible way?The greatest number of servings Rubel can create would be equal to the GCF of 245 and 294. Thus GCF of 245 and 294 is 49.
Ariel is making ready to eat meals to share with friends. She has 245 bottles of water and 294 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 245 and 294. So the GCF of 245 and 294 is 49.
Mary has 245 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 245 and 294. Hence, the GCF of 245 and 294 or the greatest arrangement is 49.
Kunal is making baskets full of nuts and dried fruits. He has 245 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 245 and 294. So the GCF of 245 and 294 is 49.