What is the definition of factors?
In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.
Properties of Factors
- Each number is a factor of itself. Eg. 38 and 56 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, 19, 38 are exact divisors of 38 and 1, 2, 4, 7, 8, 14, 28, 56 are exact divisors of 56.
- 1 is a factor of every number. Eg. 1 is a factor of 38 and also of 56.
- Every number is a factor of zero (0), since 38 x 0 = 0 and 56 x 0 = 0.
Steps to find Factors of 38 and 56
- Step 1. Find all the numbers that would divide 38 and 56 without leaving any remainder. Starting with the number 1 upto 19 (half of 38) and 1 upto 28 (half of 56). The number 1 and the number itself are always factors of the given number.
38 ÷ 1 : Remainder = 0
56 ÷ 1 : Remainder = 0
38 ÷ 2 : Remainder = 0
56 ÷ 2 : Remainder = 0
38 ÷ 19 : Remainder = 0
56 ÷ 4 : Remainder = 0
38 ÷ 38 : Remainder = 0
56 ÷ 7 : Remainder = 0
Hence, Factors of
38 are 1, 2, 19, and 38
And, Factors of
56 are 1, 2, 4, 7, 8, 14, 28, and 56
Examples of GCF
A class has 38 boys and 56 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 38 and 56. Hence, GCF of 38 and 56 is 2.
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(38, 56) = ( 38 * 56 ) / LCM(38, 56) = 2.
What is the GCF of 38 and 56?GCF of 38 and 56 is 2.
Ram has 38 cans of Pepsi and 56 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 38 and 56. Hence GCF of 38 and 56 is 2. So the number of tables that can be arranged is 2.
Rubel is creating individual servings of starters for her birthday party. He has 38 pizzas and 56 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 38 and 56. Thus GCF of 38 and 56 is 2.
Ariel is making ready to eat meals to share with friends. She has 38 bottles of water and 56 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 38 and 56. So the GCF of 38 and 56 is 2.
Mary has 38 blue buttons and 56 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 38 and 56. Hence, the GCF of 38 and 56 or the greatest arrangement is 2.
Kunal is making baskets full of nuts and dried fruits. He has 38 bags of nuts and 56 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 38 and 56. So the GCF of 38 and 56 is 2.