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 (1085, 432).
Properties of GCF
- The GCF of two or more given numbers is always less than the given numbers. Eg- GCF of 1085 and 432 is 1, where 1 is less than both the numbers.
- If the given numbers are consecutive than GCF is always 1.
- Product of two numbers is always equal to the product of their GCF and LCM.
- 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
- Every factor of a number is an exact divisor of that number, example 1, 5, 7, 31, 35, 155, 217, 1085 are exact divisors of 1085 and 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216, 432 are exact divisors of 432.
- Every number other than 1 has at least two factors, namely the number itself and 1.
- Each number is a factor of itself. Eg. 1085 and 432 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 1085 and also of 432.
Steps to find Factors of 1085 and 432
- Step 1. Find all the numbers that would divide 1085 and 432 without leaving any remainder. Starting with the number 1 upto 542 (half of 1085) and 1 upto 216 (half of 432). The number 1 and the number itself are always factors of the given number.
1085 ÷ 1 : Remainder = 0
432 ÷ 1 : Remainder = 0
1085 ÷ 5 : Remainder = 0
432 ÷ 2 : Remainder = 0
1085 ÷ 7 : Remainder = 0
432 ÷ 3 : Remainder = 0
1085 ÷ 31 : Remainder = 0
432 ÷ 4 : Remainder = 0
1085 ÷ 35 : Remainder = 0
432 ÷ 6 : Remainder = 0
1085 ÷ 155 : Remainder = 0
432 ÷ 8 : Remainder = 0
1085 ÷ 217 : Remainder = 0
432 ÷ 9 : Remainder = 0
1085 ÷ 1085 : Remainder = 0
432 ÷ 12 : Remainder = 0
432 ÷ 108 : Remainder = 0
432 ÷ 144 : Remainder = 0
432 ÷ 216 : Remainder = 0
432 ÷ 432 : Remainder = 0
Hence, Factors of
1085 are 1, 5, 7, 31, 35, 155, 217, and 1085
And, Factors of
432 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216, and 432
Examples of GCF
Sammy baked 1085 chocolate cookies and 432 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 1085 and 432.
GCF of 1085 and 432 is 1.
A class has 1085 boys and 432 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 1085 and 432. Hence, GCF of 1085 and 432 is 1.
What is the relation between LCM and GCF (Greatest Common Factor)?GCF and LCM of two numbers can be related as GCF(1085, 432) = ( 1085 * 432 ) / LCM(1085, 432) = 1.
What is the GCF of 1085 and 432?GCF of 1085 and 432 is 1.
Ram has 1085 cans of Pepsi and 432 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 1085 and 432. Hence GCF of 1085 and 432 is 1. So the number of tables that can be arranged is 1.
Rubel is creating individual servings of starters for her birthday party. He has 1085 pizzas and 432 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 1085 and 432. Thus GCF of 1085 and 432 is 1.
Ariel is making ready to eat meals to share with friends. She has 1085 bottles of water and 432 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 1085 and 432. So the GCF of 1085 and 432 is 1.
Kamal is making identical balloon arrangements for a party. He has 1085 maroon balloons, and 432 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 1085 and 432. So the GCF of 1085 and 432 is 1.
To energize public transportation, Abir needs to give a few companions envelopes with transport tickets, and metro tickets in them. On the off chance that he has 1085 bus tickets and 432 metro tickets to be parted similarly among the envelopes, and he need no tickets left. What is the greatest number of envelopes Abir can make?To make the greatest number of envelopes Abir needs to find out the GCF of 1085 and 432. Hence, GCF of 1085 and 432 is 1.