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. 1760 and 1400 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 1760 and also of 1400.
- Every number is a factor of zero (0), since 1760 x 0 = 0 and 1400 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, 8, 10, 11, 16, 20, 22, 32, 40, 44, 55, 80, 88, 110, 160, 176, 220, 352, 440, 880, 1760 are exact divisors of 1760 and 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700, 1400 are exact divisors of 1400.
- Factors of 1760 are 1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 32, 40, 44, 55, 80, 88, 110, 160, 176, 220, 352, 440, 880, 1760. Each factor divides 1760 without leaving a remainder.
Simlarly, factors of 1400 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700, 1400. Each factor divides 1400 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 32, 40, 44, 55, 80, 88, 110, 160, 176, 220, 352, 440, 880, 1760 are all less than or equal to 1760 and 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700, 1400 are all less than or equal to 1400.
Steps to find Factors of 1760 and 1400
- Step 1. Find all the numbers that would divide 1760 and 1400 without leaving any remainder. Starting with the number 1 upto 880 (half of 1760) and 1 upto 700 (half of 1400). The number 1 and the number itself are always factors of the given number.
1760 ÷ 1 : Remainder = 0
1400 ÷ 1 : Remainder = 0
1760 ÷ 2 : Remainder = 0
1400 ÷ 2 : Remainder = 0
1760 ÷ 4 : Remainder = 0
1400 ÷ 4 : Remainder = 0
1760 ÷ 5 : Remainder = 0
1400 ÷ 5 : Remainder = 0
1760 ÷ 8 : Remainder = 0
1400 ÷ 7 : Remainder = 0
1760 ÷ 10 : Remainder = 0
1400 ÷ 8 : Remainder = 0
1760 ÷ 11 : Remainder = 0
1400 ÷ 10 : Remainder = 0
1760 ÷ 16 : Remainder = 0
1400 ÷ 14 : Remainder = 0
1760 ÷ 20 : Remainder = 0
1400 ÷ 20 : Remainder = 0
1760 ÷ 22 : Remainder = 0
1400 ÷ 25 : Remainder = 0
1760 ÷ 32 : Remainder = 0
1400 ÷ 28 : Remainder = 0
1760 ÷ 40 : Remainder = 0
1400 ÷ 35 : Remainder = 0
1760 ÷ 44 : Remainder = 0
1400 ÷ 40 : Remainder = 0
1760 ÷ 55 : Remainder = 0
1400 ÷ 50 : Remainder = 0
1760 ÷ 80 : Remainder = 0
1400 ÷ 56 : Remainder = 0
1760 ÷ 88 : Remainder = 0
1400 ÷ 70 : Remainder = 0
1760 ÷ 110 : Remainder = 0
1400 ÷ 100 : Remainder = 0
1760 ÷ 160 : Remainder = 0
1400 ÷ 140 : Remainder = 0
1760 ÷ 176 : Remainder = 0
1400 ÷ 175 : Remainder = 0
1760 ÷ 220 : Remainder = 0
1400 ÷ 200 : Remainder = 0
1760 ÷ 352 : Remainder = 0
1400 ÷ 280 : Remainder = 0
1760 ÷ 440 : Remainder = 0
1400 ÷ 350 : Remainder = 0
1760 ÷ 880 : Remainder = 0
1400 ÷ 700 : Remainder = 0
1760 ÷ 1760 : Remainder = 0
1400 ÷ 1400 : Remainder = 0
Hence, Factors of
1760 are 1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 32, 40, 44, 55, 80, 88, 110, 160, 176, 220, 352, 440, 880, and 1760
And, Factors of
1400 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700, and 1400
Examples of GCF
Sammy baked 1760 chocolate cookies and 1400 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 1760 and 1400.
GCF of 1760 and 1400 is 40.
A class has 1760 boys and 1400 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 1760 and 1400. Hence, GCF of 1760 and 1400 is 40.
What is the relation between LCM and GCF (Greatest Common Factor)?GCF and LCM of two numbers can be related as GCF(1760, 1400) = ( 1760 * 1400 ) / LCM(1760, 1400) = 40.
What is the GCF of 1760 and 1400?GCF of 1760 and 1400 is 40.
Ram has 1760 cans of Pepsi and 1400 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 1760 and 1400. Hence GCF of 1760 and 1400 is 40. So the number of tables that can be arranged is 40.
Rubel is creating individual servings of starters for her birthday party. He has 1760 pizzas and 1400 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 1760 and 1400. Thus GCF of 1760 and 1400 is 40.
Ariel is making ready to eat meals to share with friends. She has 1760 bottles of water and 1400 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 1760 and 1400. So the GCF of 1760 and 1400 is 40.
Kamal is making identical balloon arrangements for a party. He has 1760 maroon balloons, and 1400 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 1760 and 1400. So the GCF of 1760 and 1400 is 40.
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 1760 bus tickets and 1400 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 1760 and 1400. Hence, GCF of 1760 and 1400 is 40.