How can we define factors?
In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.
Properties of Factors
- Each number is a factor of itself. Eg. 56 and 72 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 56 and also of 72.
- Every number is a factor of zero (0), since 56 x 0 = 0 and 72 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, 28, 56 are exact divisors of 56 and 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 are exact divisors of 72.
- Factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56. Each factor divides 56 without leaving a remainder.
Simlarly, factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. Each factor divides 72 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 7, 8, 14, 28, 56 are all less than or equal to 56 and 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 are all less than or equal to 72.
Steps to find Factors of 56 and 72
- Step 1. Find all the numbers that would divide 56 and 72 without leaving any remainder. Starting with the number 1 upto 28 (half of 56) and 1 upto 36 (half of 72). The number 1 and the number itself are always factors of the given number.
56 ÷ 1 : Remainder = 0
72 ÷ 1 : Remainder = 0
56 ÷ 2 : Remainder = 0
72 ÷ 2 : Remainder = 0
56 ÷ 4 : Remainder = 0
72 ÷ 3 : Remainder = 0
56 ÷ 7 : Remainder = 0
72 ÷ 4 : Remainder = 0
56 ÷ 8 : Remainder = 0
72 ÷ 6 : Remainder = 0
56 ÷ 14 : Remainder = 0
72 ÷ 8 : Remainder = 0
56 ÷ 28 : Remainder = 0
72 ÷ 9 : Remainder = 0
56 ÷ 56 : Remainder = 0
72 ÷ 12 : Remainder = 0
Hence, Factors of
56 are 1, 2, 4, 7, 8, 14, 28, and 56
And, Factors of
72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72
Examples of GCF
A class has 56 boys and 72 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 56 and 72. Hence, GCF of 56 and 72 is 8.
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(56, 72) = ( 56 * 72 ) / LCM(56, 72) = 8.
What is the GCF of 56 and 72?GCF of 56 and 72 is 8.
Ram has 56 cans of Pepsi and 72 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 56 and 72. Hence GCF of 56 and 72 is 8. So the number of tables that can be arranged is 8.
Rubel is creating individual servings of starters for her birthday party. He has 56 pizzas and 72 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 56 and 72. Thus GCF of 56 and 72 is 8.
Ariel is making ready to eat meals to share with friends. She has 56 bottles of water and 72 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 56 and 72. So the GCF of 56 and 72 is 8.
Mary has 56 blue buttons and 72 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 56 and 72. Hence, the GCF of 56 and 72 or the greatest arrangement is 8.
Kunal is making baskets full of nuts and dried fruits. He has 56 bags of nuts and 72 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 56 and 72. So the GCF of 56 and 72 is 8.