What is GCF of 126 and 189?


Steps to find GCF of 126 and 189

Example: Find gcf of 126 and 189

  • Factors for 126: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126
  • Factors for 189: 1, 3, 7, 9, 21, 27, 63, 189

Hence, GCf of 126 and 189 is 63

What is GCF of two numbers?

In mathematics GCF or also known as greatest common factor of two or more number is that one largest number which is a factor of those given numbers. It is represented as GCF (126, 189).

Properties of GCF

  • Given two numbers 126 and 189, such that GCF is 63 where 63 will always be less than 126 and 189.
  • GCF of two numbers is always equal to 1 in case given numbers are consecutive.
  • The product of GCF and LCM of two given numbers is equal to the product of two numbers.
  • The GCF of two given numbers is either 1 or the number itself if one of them is a prime number.

How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

Properties of Factors

  • Each number is a factor of itself. Eg. 126 and 189 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, 6, 7, 9, 14, 18, 21, 42, 63, 126 are exact divisors of 126 and 1, 3, 7, 9, 21, 27, 63, 189 are exact divisors of 189.
  • 1 is a factor of every number. Eg. 1 is a factor of 126 and also of 189.
  • Every number is a factor of zero (0), since 126 x 0 = 0 and 189 x 0 = 0.

Steps to find Factors of 126 and 189

  • Step 1. Find all the numbers that would divide 126 and 189 without leaving any remainder. Starting with the number 1 upto 63 (half of 126) and 1 upto 94 (half of 189). The number 1 and the number itself are always factors of the given number.
    126 ÷ 1 : Remainder = 0
    189 ÷ 1 : Remainder = 0
    126 ÷ 2 : Remainder = 0
    189 ÷ 3 : Remainder = 0
    126 ÷ 3 : Remainder = 0
    189 ÷ 7 : Remainder = 0
    126 ÷ 6 : Remainder = 0
    189 ÷ 9 : Remainder = 0
    126 ÷ 7 : Remainder = 0
    189 ÷ 21 : Remainder = 0
    126 ÷ 9 : Remainder = 0
    189 ÷ 27 : Remainder = 0
    126 ÷ 14 : Remainder = 0
    189 ÷ 63 : Remainder = 0
    126 ÷ 18 : Remainder = 0
    189 ÷ 189 : Remainder = 0
    126 ÷ 21 : Remainder = 0
    126 ÷ 42 : Remainder = 0
    126 ÷ 63 : Remainder = 0
    126 ÷ 126 : Remainder = 0

Hence, Factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, and 126

And, Factors of 189 are 1, 3, 7, 9, 21, 27, 63, and 189

Examples of GCF

Sammy baked 126 chocolate cookies and 189 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 126 and 189.
GCF of 126 and 189 is 63.

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(126, 189) = ( 126 * 189 ) / LCM(126, 189) = 63.

What is the GCF of 126 and 189?

GCF of 126 and 189 is 63.

Ram has 126 cans of Pepsi and 189 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 126 and 189. Hence GCF of 126 and 189 is 63. So the number of tables that can be arranged is 63.

Rubel is creating individual servings of starters for her birthday party. He has 126 pizzas and 189 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 126 and 189. Thus GCF of 126 and 189 is 63.

Ariel is making ready to eat meals to share with friends. She has 126 bottles of water and 189 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 126 and 189. So the GCF of 126 and 189 is 63.

Mary has 126 blue buttons and 189 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 126 and 189. Hence, the GCF of 126 and 189 or the greatest arrangement is 63.

Kamal is making identical balloon arrangements for a party. He has 126 maroon balloons, and 189 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 126 and 189. So the GCF of 126 and 189 is 63.