What is GCF of 1225 and 105?

Go back to 'All gcf of pages' >

GCF of 1225 and 105 is 35

How to find GCF of two numbers

Steps to find GCF of 1225 and 105

Find all the numbers that would divide 1225 and 105 without leaving any remainder as explained in factors below.
Find the greatest common factor from the list of factors for 1225 and 105, and read off the answer!

Example: Find gcf of 1225 and 105

Factors for 1225: 1, 5, 7, 25, 35, 49, 175, 245, 1225
Factors for 105: 1, 3, 5, 7, 15, 21, 35, 105

Hence, GCf of 1225 and 105 is 35

Definition of GCF

Greatest common factor commonly known as GCF of the two numbers is the highest possible number which completely divides given numbers, i.e. without leaving any remainder. It is represented as GCF (1225, 105).

Properties of GCF

The GCF of two or more given numbers is always less than the given numbers. Eg- GCF of 1225 and 105 is 35, where 35 is less than both the numbers.
If the given numbers are consecutive than GCF is always 1.
Product of two numbers is always equal to the product of their GCF and LCM.
The GCF of two given numbers where one of them is a prime number is either 1 or the number itself.

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

Every factor of a number is an exact divisor of that number, example 1, 5, 7, 25, 35, 49, 175, 245, 1225 are exact divisors of 1225 and 1, 3, 5, 7, 15, 21, 35, 105 are exact divisors of 105.
Every number other than 1 has at least two factors, namely the number itself and 1.
Each number is a factor of itself. Eg. 1225 and 105 are factors of themselves respectively.
1 is a factor of every number. Eg. 1 is a factor of 1225 and also of 105.

Steps to find Factors of 1225 and 105

Step 1. Find all the numbers that would divide 1225 and 105 without leaving any remainder. Starting with the number 1 upto 612 (half of 1225) and 1 upto 52 (half of 105). The number 1 and the number itself are always factors of the given number.

1225 ÷ 1 : Remainder = 0

105 ÷ 1 : Remainder = 0

1225 ÷ 5 : Remainder = 0

105 ÷ 3 : Remainder = 0

1225 ÷ 7 : Remainder = 0

105 ÷ 5 : Remainder = 0

1225 ÷ 25 : Remainder = 0

105 ÷ 7 : Remainder = 0

1225 ÷ 35 : Remainder = 0

105 ÷ 15 : Remainder = 0

1225 ÷ 49 : Remainder = 0

105 ÷ 21 : Remainder = 0

1225 ÷ 175 : Remainder = 0

105 ÷ 35 : Remainder = 0

1225 ÷ 245 : Remainder = 0

105 ÷ 105 : Remainder = 0

1225 ÷ 1225 : Remainder = 0

Hence, Factors of 1225 are 1, 5, 7, 25, 35, 49, 175, 245, and 1225

And, Factors of 105 are 1, 3, 5, 7, 15, 21, 35, and 105

Examples of GCF

Sammy baked 1225 chocolate cookies and 105 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 1225 and 105.
GCF of 1225 and 105 is 35.

A class has 1225 boys and 105 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 1225 and 105. Hence, GCF of 1225 and 105 is 35.

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

GCF and LCM of two numbers can be related as GCF(1225, 105) = ( 1225 * 105 ) / LCM(1225, 105) = 35.

What is the GCF of 1225 and 105?

GCF of 1225 and 105 is 35.

Ram has 1225 cans of Pepsi and 105 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 1225 and 105. Hence GCF of 1225 and 105 is 35. So the number of tables that can be arranged is 35.

Mary has 1225 blue buttons and 105 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 1225 and 105. Hence, the GCF of 1225 and 105 or the greatest arrangement is 35.

Kamal is making identical balloon arrangements for a party. He has 1225 maroon balloons, and 105 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 1225 and 105. So the GCF of 1225 and 105 is 35.

Kunal is making baskets full of nuts and dried fruits. He has 1225 bags of nuts and 105 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 1225 and 105. So the GCF of 1225 and 105 is 35.

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 1225 bus tickets and 105 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 1225 and 105. Hence, GCF of 1225 and 105 is 35.