What is GCF of 17 and 51?

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GCF of 17 and 51 is 17

How to find GCF of two numbers

Steps to find GCF of 17 and 51

Find all the numbers that would divide 17 and 51 without leaving any remainder as explained in factors below.
Find the greatest common factor from the list of factors for 17 and 51, and read off the answer!

Example: Find gcf of 17 and 51

Factors for 17: 1, 17
Factors for 51: 1, 3, 17, 51

Hence, GCf of 17 and 51 is 17

How do we define GCF?

In mathematics we use GCF or greatest common method to find out the greatest possible positive integer which can completely divide the given numbers. It is written as GCF (17, 51).

Properties of GCF

The GCF of two or more given numbers is always less than the given numbers. Eg- GCF of 17 and 51 is 17, where 17 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.

How do you explain factors?

In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any 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, 17 are exact divisors of 17 and 1, 3, 17, 51 are exact divisors of 51.
Every number other than 1 has at least two factors, namely the number itself and 1.
Each number is a factor of itself. Eg. 17 and 51 are factors of themselves respectively.
1 is a factor of every number. Eg. 1 is a factor of 17 and also of 51.

Steps to find Factors of 17 and 51

Step 1. Find all the numbers that would divide 17 and 51 without leaving any remainder. Starting with the number 1 upto 8 (half of 17) and 1 upto 25 (half of 51). The number 1 and the number itself are always factors of the given number.

17 ÷ 1 : Remainder = 0

51 ÷ 1 : Remainder = 0

17 ÷ 17 : Remainder = 0

51 ÷ 3 : Remainder = 0

51 ÷ 17 : Remainder = 0

51 ÷ 51 : Remainder = 0

Hence, Factors of 17 are 1 and 17

And, Factors of 51 are 1, 3, 17, and 51

Examples of GCF

Sammy baked 17 chocolate cookies and 51 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 17 and 51.
GCF of 17 and 51 is 17.

A class has 17 boys and 51 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 17 and 51. Hence, GCF of 17 and 51 is 17.

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(17, 51) = ( 17 * 51 ) / LCM(17, 51) = 17.

What is the GCF of 17 and 51?

GCF of 17 and 51 is 17.

Ariel is making ready to eat meals to share with friends. She has 17 bottles of water and 51 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 17 and 51. So the GCF of 17 and 51 is 17.

Mary has 17 blue buttons and 51 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 17 and 51. Hence, the GCF of 17 and 51 or the greatest arrangement is 17.

Kamal is making identical balloon arrangements for a party. He has 17 maroon balloons, and 51 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 17 and 51. So the GCF of 17 and 51 is 17.

Kunal is making baskets full of nuts and dried fruits. He has 17 bags of nuts and 51 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 17 and 51. So the GCF of 17 and 51 is 17.