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 (340, 350).
Properties of GCF
- The GCF of two or more given numbers cannot be greater than any of the given number. Eg- GCF of 340 and 350 is 10, where 10 is less than both 340 and 350.
- GCF of two consecutive numbers is always 1.
- The product of GCF and LCM of two given numbers is equal to the product of two numbers.
- 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
- Each number is a factor of itself. Eg. 340 and 350 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 340 and also of 350.
- Every number is a factor of zero (0), since 340 x 0 = 0 and 350 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, 5, 10, 17, 20, 34, 68, 85, 170, 340 are exact divisors of 340 and 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350 are exact divisors of 350.
- Factors of 340 are 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, 340. Each factor divides 340 without leaving a remainder.
Simlarly, factors of 350 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350. Each factor divides 350 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, 340 are all less than or equal to 340 and 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350 are all less than or equal to 350.
Steps to find Factors of 340 and 350
- Step 1. Find all the numbers that would divide 340 and 350 without leaving any remainder. Starting with the number 1 upto 170 (half of 340) and 1 upto 175 (half of 350). The number 1 and the number itself are always factors of the given number.
340 ÷ 1 : Remainder = 0
350 ÷ 1 : Remainder = 0
340 ÷ 2 : Remainder = 0
350 ÷ 2 : Remainder = 0
340 ÷ 4 : Remainder = 0
350 ÷ 5 : Remainder = 0
340 ÷ 5 : Remainder = 0
350 ÷ 7 : Remainder = 0
340 ÷ 10 : Remainder = 0
350 ÷ 10 : Remainder = 0
340 ÷ 17 : Remainder = 0
350 ÷ 14 : Remainder = 0
340 ÷ 20 : Remainder = 0
350 ÷ 25 : Remainder = 0
340 ÷ 34 : Remainder = 0
350 ÷ 35 : Remainder = 0
340 ÷ 68 : Remainder = 0
350 ÷ 50 : Remainder = 0
340 ÷ 85 : Remainder = 0
350 ÷ 70 : Remainder = 0
340 ÷ 170 : Remainder = 0
350 ÷ 175 : Remainder = 0
340 ÷ 340 : Remainder = 0
350 ÷ 350 : Remainder = 0
Hence, Factors of
340 are 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, and 340
And, Factors of
350 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, and 350
Examples of GCF
Sammy baked 340 chocolate cookies and 350 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 340 and 350.
GCF of 340 and 350 is 10.
A class has 340 boys and 350 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 340 and 350. Hence, GCF of 340 and 350 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(340, 350) = ( 340 * 350 ) / LCM(340, 350) = 10.
What is the GCF of 340 and 350?GCF of 340 and 350 is 10.
Ariel is making ready to eat meals to share with friends. She has 340 bottles of water and 350 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 340 and 350. So the GCF of 340 and 350 is 10.
Mary has 340 blue buttons and 350 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 340 and 350. Hence, the GCF of 340 and 350 or the greatest arrangement is 10.
Kamal is making identical balloon arrangements for a party. He has 340 maroon balloons, and 350 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 340 and 350. So the GCF of 340 and 350 is 10.
Kunal is making baskets full of nuts and dried fruits. He has 340 bags of nuts and 350 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 340 and 350. So the GCF of 340 and 350 is 10.