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. 420 and 450 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 420 and also of 450.
- Every number is a factor of zero (0), since 420 x 0 = 0 and 450 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, 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 and 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450 are exact divisors of 450.
- 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.
Simlarly, factors of 450 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450. Each factor divides 450 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 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 all less than or equal to 420 and 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450 are all less than or equal to 450.
Steps to find Factors of 420 and 450
- Step 1. Find all the numbers that would divide 420 and 450 without leaving any remainder. Starting with the number 1 upto 210 (half of 420) and 1 upto 225 (half of 450). The number 1 and the number itself are always factors of the given number.
420 ÷ 1 : Remainder = 0
450 ÷ 1 : Remainder = 0
420 ÷ 2 : Remainder = 0
450 ÷ 2 : Remainder = 0
420 ÷ 3 : Remainder = 0
450 ÷ 3 : Remainder = 0
420 ÷ 4 : Remainder = 0
450 ÷ 5 : Remainder = 0
420 ÷ 5 : Remainder = 0
450 ÷ 6 : Remainder = 0
420 ÷ 6 : Remainder = 0
450 ÷ 9 : Remainder = 0
420 ÷ 7 : Remainder = 0
450 ÷ 10 : Remainder = 0
420 ÷ 10 : Remainder = 0
450 ÷ 15 : Remainder = 0
420 ÷ 12 : Remainder = 0
450 ÷ 18 : Remainder = 0
420 ÷ 14 : Remainder = 0
450 ÷ 25 : Remainder = 0
420 ÷ 15 : Remainder = 0
450 ÷ 30 : Remainder = 0
420 ÷ 20 : Remainder = 0
450 ÷ 45 : Remainder = 0
420 ÷ 21 : Remainder = 0
450 ÷ 50 : Remainder = 0
420 ÷ 28 : Remainder = 0
450 ÷ 75 : Remainder = 0
420 ÷ 30 : Remainder = 0
450 ÷ 90 : Remainder = 0
420 ÷ 35 : Remainder = 0
450 ÷ 150 : Remainder = 0
420 ÷ 42 : Remainder = 0
450 ÷ 225 : Remainder = 0
420 ÷ 60 : Remainder = 0
450 ÷ 450 : Remainder = 0
420 ÷ 105 : Remainder = 0
420 ÷ 140 : Remainder = 0
420 ÷ 210 : Remainder = 0
420 ÷ 420 : Remainder = 0
Hence, 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
And, Factors of
450 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, and 450
Examples of GCF
What is the relation between LCM and GCF (Greatest Common Factor)?GCF and LCM of two numbers can be related as GCF(420, 450) = ( 420 * 450 ) / LCM(420, 450) = 30.
What is the GCF of 420 and 450?GCF of 420 and 450 is 30.
Ram has 420 cans of Pepsi and 450 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 420 and 450. Hence GCF of 420 and 450 is 30. So the number of tables that can be arranged is 30.
Rubel is creating individual servings of starters for her birthday party. He has 420 pizzas and 450 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 420 and 450. Thus GCF of 420 and 450 is 30.
Ariel is making ready to eat meals to share with friends. She has 420 bottles of water and 450 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 420 and 450. So the GCF of 420 and 450 is 30.
Mary has 420 blue buttons and 450 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 420 and 450. Hence, the GCF of 420 and 450 or the greatest arrangement is 30.
Kamal is making identical balloon arrangements for a party. He has 420 maroon balloons, and 450 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 420 and 450. So the GCF of 420 and 450 is 30.
Kunal is making baskets full of nuts and dried fruits. He has 420 bags of nuts and 450 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 420 and 450. So the GCF of 420 and 450 is 30.
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 420 bus tickets and 450 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 420 and 450. Hence, GCF of 420 and 450 is 30.