How do you explain factors?
In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.
Properties of Factors
- Every number is a factor of zero (0), since 207 x 0 = 0 and 420 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, 3, 9, 23, 69, 207 are exact divisors of 207 and 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420 are exact divisors of 420.
- Factors of 207 are 1, 3, 9, 23, 69, 207. Each factor divides 207 without leaving a remainder.
Simlarly, factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420. Each factor divides 420 without leaving a remainder.
Steps to find Factors of 207 and 420
- Step 1. Find all the numbers that would divide 207 and 420 without leaving any remainder. Starting with the number 1 upto 103 (half of 207) and 1 upto 210 (half of 420). The number 1 and the number itself are always factors of the given number.
207 ÷ 1 : Remainder = 0
420 ÷ 1 : Remainder = 0
207 ÷ 3 : Remainder = 0
420 ÷ 2 : Remainder = 0
207 ÷ 9 : Remainder = 0
420 ÷ 3 : Remainder = 0
207 ÷ 23 : Remainder = 0
420 ÷ 4 : Remainder = 0
207 ÷ 69 : Remainder = 0
420 ÷ 5 : Remainder = 0
207 ÷ 207 : Remainder = 0
420 ÷ 6 : Remainder = 0
420 ÷ 105 : Remainder = 0
420 ÷ 140 : Remainder = 0
420 ÷ 210 : Remainder = 0
420 ÷ 420 : Remainder = 0
Hence, Factors of
207 are 1, 3, 9, 23, 69, and 207
And, Factors of
420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, and 420
Examples of GCF
Sammy baked 207 chocolate cookies and 420 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 207 and 420.
GCF of 207 and 420 is 3.
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(207, 420) = ( 207 * 420 ) / LCM(207, 420) = 3.
What is the GCF of 207 and 420?GCF of 207 and 420 is 3.
Ram has 207 cans of Pepsi and 420 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 207 and 420. Hence GCF of 207 and 420 is 3. So the number of tables that can be arranged is 3.
Rubel is creating individual servings of starters for her birthday party. He has 207 pizzas and 420 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 207 and 420. Thus GCF of 207 and 420 is 3.
Ariel is making ready to eat meals to share with friends. She has 207 bottles of water and 420 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 207 and 420. So the GCF of 207 and 420 is 3.
Mary has 207 blue buttons and 420 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 207 and 420. Hence, the GCF of 207 and 420 or the greatest arrangement is 3.
Kamal is making identical balloon arrangements for a party. He has 207 maroon balloons, and 420 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 207 and 420. So the GCF of 207 and 420 is 3.