What is GCF of 125 and 512?

Go back to 'All gcf of pages' >

GCF of 125 and 512 is 1

How to find GCF of two numbers

Steps to find GCF of 125 and 512

Find all the numbers that would divide 125 and 512 without leaving any remainder as explained in factors below.
Find the greatest common factor from the list of factors for 125 and 512, and read off the answer!

Example: Find gcf of 125 and 512

Factors for 125: 1, 5, 25, 125
Factors for 512: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512

Hence, GCf of 125 and 512 is 1

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 (125, 512).

Properties of GCF

The GCF of two or more given numbers is always less than the given numbers. Eg- GCF of 125 and 512 is 1, where 1 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, 25, 125 are exact divisors of 125 and 1, 2, 4, 8, 16, 32, 64, 128, 256, 512 are exact divisors of 512.
Every number other than 1 has at least two factors, namely the number itself and 1.
Each number is a factor of itself. Eg. 125 and 512 are factors of themselves respectively.
1 is a factor of every number. Eg. 1 is a factor of 125 and also of 512.

Steps to find Factors of 125 and 512

Step 1. Find all the numbers that would divide 125 and 512 without leaving any remainder. Starting with the number 1 upto 62 (half of 125) and 1 upto 256 (half of 512). The number 1 and the number itself are always factors of the given number.

125 ÷ 1 : Remainder = 0

512 ÷ 1 : Remainder = 0

125 ÷ 5 : Remainder = 0

512 ÷ 2 : Remainder = 0

125 ÷ 25 : Remainder = 0

512 ÷ 4 : Remainder = 0

125 ÷ 125 : Remainder = 0

512 ÷ 8 : Remainder = 0

512 ÷ 16 : Remainder = 0

512 ÷ 32 : Remainder = 0

512 ÷ 64 : Remainder = 0

512 ÷ 128 : Remainder = 0

512 ÷ 256 : Remainder = 0

512 ÷ 512 : Remainder = 0

Hence, Factors of 125 are 1, 5, 25, and 125

And, Factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, and 512

Examples of GCF

Sammy baked 125 chocolate cookies and 512 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 125 and 512.
GCF of 125 and 512 is 1.

A class has 125 boys and 512 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 125 and 512. Hence, GCF of 125 and 512 is 1.

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(125, 512) = ( 125 * 512 ) / LCM(125, 512) = 1.

What is the GCF of 125 and 512?

GCF of 125 and 512 is 1.

Ariel is making ready to eat meals to share with friends. She has 125 bottles of water and 512 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 125 and 512. So the GCF of 125 and 512 is 1.

Mary has 125 blue buttons and 512 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 125 and 512. Hence, the GCF of 125 and 512 or the greatest arrangement is 1.

Kamal is making identical balloon arrangements for a party. He has 125 maroon balloons, and 512 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 125 and 512. So the GCF of 125 and 512 is 1.

Kunal is making baskets full of nuts and dried fruits. He has 125 bags of nuts and 512 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 125 and 512. So the GCF of 125 and 512 is 1.