What is GCF of 1682 and 20?

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GCF of 1682 and 20 is 2

How to find GCF of two numbers

Steps to find GCF of 1682 and 20

Find all the numbers that would divide 1682 and 20 without leaving any remainder as explained in factors below.
Find the greatest common factor from the list of factors for 1682 and 20, and read off the answer!

Example: Find gcf of 1682 and 20

Factors for 1682: 1, 2, 29, 58, 841, 1682
Factors for 20: 1, 2, 4, 5, 10, 20

Hence, GCf of 1682 and 20 is 2

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 (1682, 20).

Properties of GCF

Given two numbers 1682 and 20, such that GCF is 2 where 2 will always be less than 1682 and 20.
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 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

Each number is a factor of itself. Eg. 1682 and 20 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, 29, 58, 841, 1682 are exact divisors of 1682 and 1, 2, 4, 5, 10, 20 are exact divisors of 20.
1 is a factor of every number. Eg. 1 is a factor of 1682 and also of 20.
Every number is a factor of zero (0), since 1682 x 0 = 0 and 20 x 0 = 0.

Steps to find Factors of 1682 and 20

Step 1. Find all the numbers that would divide 1682 and 20 without leaving any remainder. Starting with the number 1 upto 841 (half of 1682) and 1 upto 10 (half of 20). The number 1 and the number itself are always factors of the given number.

1682 ÷ 1 : Remainder = 0

20 ÷ 1 : Remainder = 0

1682 ÷ 2 : Remainder = 0

20 ÷ 2 : Remainder = 0

1682 ÷ 29 : Remainder = 0

20 ÷ 4 : Remainder = 0

1682 ÷ 58 : Remainder = 0

20 ÷ 5 : Remainder = 0

1682 ÷ 841 : Remainder = 0

20 ÷ 10 : Remainder = 0

1682 ÷ 1682 : Remainder = 0

20 ÷ 20 : Remainder = 0

Hence, Factors of 1682 are 1, 2, 29, 58, 841, and 1682

And, Factors of 20 are 1, 2, 4, 5, 10, and 20

Examples of GCF

Sammy baked 1682 chocolate cookies and 20 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 1682 and 20.
GCF of 1682 and 20 is 2.

A class has 1682 boys and 20 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 1682 and 20. Hence, GCF of 1682 and 20 is 2.

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(1682, 20) = ( 1682 * 20 ) / LCM(1682, 20) = 2.

What is the GCF of 1682 and 20?

GCF of 1682 and 20 is 2.

Ariel is making ready to eat meals to share with friends. She has 1682 bottles of water and 20 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 1682 and 20. So the GCF of 1682 and 20 is 2.

Mary has 1682 blue buttons and 20 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 1682 and 20. Hence, the GCF of 1682 and 20 or the greatest arrangement is 2.

Kamal is making identical balloon arrangements for a party. He has 1682 maroon balloons, and 20 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 1682 and 20. So the GCF of 1682 and 20 is 2.

Kunal is making baskets full of nuts and dried fruits. He has 1682 bags of nuts and 20 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 1682 and 20. So the GCF of 1682 and 20 is 2.