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. 1890 and 4900 are factors of themselves respectively.
- 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, 5, 6, 7, 9, 10, 14, 15, 18, 21, 27, 30, 35, 42, 45, 54, 63, 70, 90, 105, 126, 135, 189, 210, 270, 315, 378, 630, 945, 1890 are exact divisors of 1890 and 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 49, 50, 70, 98, 100, 140, 175, 196, 245, 350, 490, 700, 980, 1225, 2450, 4900 are exact divisors of 4900.
- 1 is a factor of every number. Eg. 1 is a factor of 1890 and also of 4900.
- Every number is a factor of zero (0), since 1890 x 0 = 0 and 4900 x 0 = 0.
Steps to find Factors of 1890 and 4900
- Step 1. Find all the numbers that would divide 1890 and 4900 without leaving any remainder. Starting with the number 1 upto 945 (half of 1890) and 1 upto 2450 (half of 4900). The number 1 and the number itself are always factors of the given number.
1890 ÷ 1 : Remainder = 0
4900 ÷ 1 : Remainder = 0
1890 ÷ 2 : Remainder = 0
4900 ÷ 2 : Remainder = 0
1890 ÷ 3 : Remainder = 0
4900 ÷ 4 : Remainder = 0
1890 ÷ 5 : Remainder = 0
4900 ÷ 5 : Remainder = 0
1890 ÷ 6 : Remainder = 0
4900 ÷ 7 : Remainder = 0
1890 ÷ 7 : Remainder = 0
4900 ÷ 10 : Remainder = 0
1890 ÷ 9 : Remainder = 0
4900 ÷ 14 : Remainder = 0
1890 ÷ 10 : Remainder = 0
4900 ÷ 20 : Remainder = 0
1890 ÷ 14 : Remainder = 0
4900 ÷ 25 : Remainder = 0
1890 ÷ 15 : Remainder = 0
4900 ÷ 28 : Remainder = 0
1890 ÷ 18 : Remainder = 0
4900 ÷ 35 : Remainder = 0
1890 ÷ 21 : Remainder = 0
4900 ÷ 49 : Remainder = 0
1890 ÷ 27 : Remainder = 0
4900 ÷ 50 : Remainder = 0
1890 ÷ 30 : Remainder = 0
4900 ÷ 70 : Remainder = 0
1890 ÷ 35 : Remainder = 0
4900 ÷ 98 : Remainder = 0
1890 ÷ 42 : Remainder = 0
4900 ÷ 100 : Remainder = 0
1890 ÷ 45 : Remainder = 0
4900 ÷ 140 : Remainder = 0
1890 ÷ 54 : Remainder = 0
4900 ÷ 175 : Remainder = 0
1890 ÷ 63 : Remainder = 0
4900 ÷ 196 : Remainder = 0
1890 ÷ 70 : Remainder = 0
4900 ÷ 245 : Remainder = 0
1890 ÷ 90 : Remainder = 0
4900 ÷ 350 : Remainder = 0
1890 ÷ 105 : Remainder = 0
4900 ÷ 490 : Remainder = 0
1890 ÷ 126 : Remainder = 0
4900 ÷ 700 : Remainder = 0
1890 ÷ 135 : Remainder = 0
4900 ÷ 980 : Remainder = 0
1890 ÷ 189 : Remainder = 0
4900 ÷ 1225 : Remainder = 0
1890 ÷ 210 : Remainder = 0
4900 ÷ 2450 : Remainder = 0
1890 ÷ 270 : Remainder = 0
4900 ÷ 4900 : Remainder = 0
1890 ÷ 315 : Remainder = 0
1890 ÷ 378 : Remainder = 0
1890 ÷ 630 : Remainder = 0
1890 ÷ 945 : Remainder = 0
1890 ÷ 1890 : Remainder = 0
Hence, Factors of
1890 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 27, 30, 35, 42, 45, 54, 63, 70, 90, 105, 126, 135, 189, 210, 270, 315, 378, 630, 945, and 1890
And, Factors of
4900 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 49, 50, 70, 98, 100, 140, 175, 196, 245, 350, 490, 700, 980, 1225, 2450, and 4900
Examples of GCF
Sammy baked 1890 chocolate cookies and 4900 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 1890 and 4900.
GCF of 1890 and 4900 is 70.
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(1890, 4900) = ( 1890 * 4900 ) / LCM(1890, 4900) = 70.
What is the GCF of 1890 and 4900?GCF of 1890 and 4900 is 70.
Ram has 1890 cans of Pepsi and 4900 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 1890 and 4900. Hence GCF of 1890 and 4900 is 70. So the number of tables that can be arranged is 70.
Rubel is creating individual servings of starters for her birthday party. He has 1890 pizzas and 4900 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 1890 and 4900. Thus GCF of 1890 and 4900 is 70.
Ariel is making ready to eat meals to share with friends. She has 1890 bottles of water and 4900 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 1890 and 4900. So the GCF of 1890 and 4900 is 70.
Mary has 1890 blue buttons and 4900 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 1890 and 4900. Hence, the GCF of 1890 and 4900 or the greatest arrangement is 70.
Kamal is making identical balloon arrangements for a party. He has 1890 maroon balloons, and 4900 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 1890 and 4900. So the GCF of 1890 and 4900 is 70.