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 (34, 42).
Properties of GCF
- Given two numbers 34 and 42, such that GCF is 2 where 2 will always be less than 34 and 42.
- 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. 34 and 42 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, 17, 34 are exact divisors of 34 and 1, 2, 3, 6, 7, 14, 21, 42 are exact divisors of 42.
- 1 is a factor of every number. Eg. 1 is a factor of 34 and also of 42.
- Every number is a factor of zero (0), since 34 x 0 = 0 and 42 x 0 = 0.
Steps to find Factors of 34 and 42
- Step 1. Find all the numbers that would divide 34 and 42 without leaving any remainder. Starting with the number 1 upto 17 (half of 34) and 1 upto 21 (half of 42). The number 1 and the number itself are always factors of the given number.
34 ÷ 1 : Remainder = 0
42 ÷ 1 : Remainder = 0
34 ÷ 2 : Remainder = 0
42 ÷ 2 : Remainder = 0
34 ÷ 17 : Remainder = 0
42 ÷ 3 : Remainder = 0
34 ÷ 34 : Remainder = 0
42 ÷ 6 : Remainder = 0
Hence, Factors of
34 are 1, 2, 17, and 34
And, Factors of
42 are 1, 2, 3, 6, 7, 14, 21, and 42
Examples of GCF
Sammy baked 34 chocolate cookies and 42 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 34 and 42.
GCF of 34 and 42 is 2.
A class has 34 boys and 42 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 34 and 42. Hence, GCF of 34 and 42 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(34, 42) = ( 34 * 42 ) / LCM(34, 42) = 2.
What is the GCF of 34 and 42?GCF of 34 and 42 is 2.
Ariel is making ready to eat meals to share with friends. She has 34 bottles of water and 42 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 34 and 42. So the GCF of 34 and 42 is 2.
Mary has 34 blue buttons and 42 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 34 and 42. Hence, the GCF of 34 and 42 or the greatest arrangement is 2.
Kamal is making identical balloon arrangements for a party. He has 34 maroon balloons, and 42 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 34 and 42. So the GCF of 34 and 42 is 2.
Kunal is making baskets full of nuts and dried fruits. He has 34 bags of nuts and 42 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 34 and 42. So the GCF of 34 and 42 is 2.