# What is GCF of 28 and 70?

GCF of 28 and 70 is 14

#### How to find GCF of two numbers

 1.   Steps to find GCF of 28 and 70 2.   What is GCF of two numbers? 3.   What are Factors? 4.   Examples of GCF

### Example: Find gcf of 28 and 70

• Factors for 28: 1, 2, 4, 7, 14, 28
• Factors for 70: 1, 2, 5, 7, 10, 14, 35, 70

Hence, GCf of 28 and 70 is 14

#### What does GCF mean in mathematics?

Greatest Common Fcator (GCF) or also sometimes written as greates common divisor is the largest number that can evenly divide the given two numbers. GCF is represented as GCF (28, 70).

#### Properties of GCF

• The GCF of two or more given numbers cannot be greater than any of the given number. Eg- GCF of 28 and 70 is 14, where 14 is less than both 28 and 70.
• GCF of two consecutive numbers is always 1.
• The product of GCF and LCM of two given numbers is equal to the product of two numbers.
• The GCF of two given numbers where one of them is a prime number is either 1 or the number itself.

#### What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

#### Properties of Factors

• Each number is a factor of itself. Eg. 28 and 70 are factors of themselves respectively.
• 1 is a factor of every number. Eg. 1 is a factor of 28 and also of 70.
• Every number is a factor of zero (0), since 28 x 0 = 0 and 70 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, 7, 14, 28 are exact divisors of 28 and 1, 2, 5, 7, 10, 14, 35, 70 are exact divisors of 70.
• Factors of 28 are 1, 2, 4, 7, 14, 28. Each factor divides 28 without leaving a remainder.
Simlarly, factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70. Each factor divides 70 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 7, 14, 28 are all less than or equal to 28 and 1, 2, 5, 7, 10, 14, 35, 70 are all less than or equal to 70.

#### Steps to find Factors of 28 and 70

• Step 1. Find all the numbers that would divide 28 and 70 without leaving any remainder. Starting with the number 1 upto 14 (half of 28) and 1 upto 35 (half of 70). The number 1 and the number itself are always factors of the given number.
28 ÷ 1 : Remainder = 0
70 ÷ 1 : Remainder = 0
28 ÷ 2 : Remainder = 0
70 ÷ 2 : Remainder = 0
28 ÷ 4 : Remainder = 0
70 ÷ 5 : Remainder = 0
28 ÷ 7 : Remainder = 0
70 ÷ 7 : Remainder = 0
28 ÷ 14 : Remainder = 0
70 ÷ 10 : Remainder = 0
28 ÷ 28 : Remainder = 0
70 ÷ 14 : Remainder = 0
70 ÷ 35 : Remainder = 0
70 ÷ 70 : Remainder = 0

Hence, Factors of 28 are 1, 2, 4, 7, 14, and 28

And, Factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70

#### Examples of GCF

Sammy baked 28 chocolate cookies and 70 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 28 and 70.
GCF of 28 and 70 is 14.

A class has 28 boys and 70 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 28 and 70. Hence, GCF of 28 and 70 is 14.

What is the relation between LCM and GCF (Greatest Common Factor)?

GCF and LCM of two numbers can be related as GCF(28, 70) = ( 28 * 70 ) / LCM(28, 70) = 14.

What is the GCF of 28 and 70?

GCF of 28 and 70 is 14.

Ram has 28 cans of Pepsi and 70 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 28 and 70. Hence GCF of 28 and 70 is 14. So the number of tables that can be arranged is 14.

Mary has 28 blue buttons and 70 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 28 and 70. Hence, the GCF of 28 and 70 or the greatest arrangement is 14.

Kamal is making identical balloon arrangements for a party. He has 28 maroon balloons, and 70 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 28 and 70. So the GCF of 28 and 70 is 14.

Kunal is making baskets full of nuts and dried fruits. He has 28 bags of nuts and 70 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 28 and 70. So the GCF of 28 and 70 is 14.

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 28 bus tickets and 70 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 28 and 70. Hence, GCF of 28 and 70 is 14.