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 (170, 210).
Properties of GCF
- Given two numbers 170 and 210, such that GCF is 10 where 10 will always be less than 170 and 210.
- 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.
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
- Each number is a factor of itself. Eg. 170 and 210 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, 5, 10, 17, 34, 85, 170 are exact divisors of 170 and 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210 are exact divisors of 210.
- 1 is a factor of every number. Eg. 1 is a factor of 170 and also of 210.
- Every number is a factor of zero (0), since 170 x 0 = 0 and 210 x 0 = 0.
Steps to find Factors of 170 and 210
- Step 1. Find all the numbers that would divide 170 and 210 without leaving any remainder. Starting with the number 1 upto 85 (half of 170) and 1 upto 105 (half of 210). The number 1 and the number itself are always factors of the given number.
170 ÷ 1 : Remainder = 0
210 ÷ 1 : Remainder = 0
170 ÷ 2 : Remainder = 0
210 ÷ 2 : Remainder = 0
170 ÷ 5 : Remainder = 0
210 ÷ 3 : Remainder = 0
170 ÷ 10 : Remainder = 0
210 ÷ 5 : Remainder = 0
170 ÷ 17 : Remainder = 0
210 ÷ 6 : Remainder = 0
170 ÷ 34 : Remainder = 0
210 ÷ 7 : Remainder = 0
170 ÷ 85 : Remainder = 0
210 ÷ 10 : Remainder = 0
170 ÷ 170 : Remainder = 0
210 ÷ 14 : Remainder = 0
210 ÷ 105 : Remainder = 0
210 ÷ 210 : Remainder = 0
Hence, Factors of
170 are 1, 2, 5, 10, 17, 34, 85, and 170
And, Factors of
210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, and 210
Examples of GCF
Sammy baked 170 chocolate cookies and 210 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 170 and 210.
GCF of 170 and 210 is 10.
A class has 170 boys and 210 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 170 and 210. Hence, GCF of 170 and 210 is 10.
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(170, 210) = ( 170 * 210 ) / LCM(170, 210) = 10.
What is the GCF of 170 and 210?GCF of 170 and 210 is 10.
Ariel is making ready to eat meals to share with friends. She has 170 bottles of water and 210 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 170 and 210. So the GCF of 170 and 210 is 10.
Mary has 170 blue buttons and 210 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 170 and 210. Hence, the GCF of 170 and 210 or the greatest arrangement is 10.
Kamal is making identical balloon arrangements for a party. He has 170 maroon balloons, and 210 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 170 and 210. So the GCF of 170 and 210 is 10.
Kunal is making baskets full of nuts and dried fruits. He has 170 bags of nuts and 210 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 170 and 210. So the GCF of 170 and 210 is 10.
A class has 170 boys and 210 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 170 and 210. Hence, GCF of 170 and 210 is 10.