What is GCF of 102 and 170?

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GCF of 102 and 170 is 34

How to find GCF of two numbers

Steps to find GCF of 102 and 170

Find all the numbers that would divide 102 and 170 without leaving any remainder as explained in factors below.
Find the greatest common factor from the list of factors for 102 and 170, and read off the answer!

Example: Find gcf of 102 and 170

Factors for 102: 1, 2, 3, 6, 17, 34, 51, 102
Factors for 170: 1, 2, 5, 10, 17, 34, 85, 170

Hence, GCf of 102 and 170 is 34

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 (102, 170).

Properties of GCF

Given two numbers 102 and 170, such that GCF is 34 where 34 will always be less than 102 and 170.
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. 102 and 170 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, 3, 6, 17, 34, 51, 102 are exact divisors of 102 and 1, 2, 5, 10, 17, 34, 85, 170 are exact divisors of 170.
1 is a factor of every number. Eg. 1 is a factor of 102 and also of 170.
Every number is a factor of zero (0), since 102 x 0 = 0 and 170 x 0 = 0.

Steps to find Factors of 102 and 170

Step 1. Find all the numbers that would divide 102 and 170 without leaving any remainder. Starting with the number 1 upto 51 (half of 102) and 1 upto 85 (half of 170). The number 1 and the number itself are always factors of the given number.

102 ÷ 1 : Remainder = 0

170 ÷ 1 : Remainder = 0

102 ÷ 2 : Remainder = 0

170 ÷ 2 : Remainder = 0

102 ÷ 3 : Remainder = 0

170 ÷ 5 : Remainder = 0

102 ÷ 6 : Remainder = 0

170 ÷ 10 : Remainder = 0

102 ÷ 17 : Remainder = 0

170 ÷ 17 : Remainder = 0

102 ÷ 34 : Remainder = 0

170 ÷ 34 : Remainder = 0

102 ÷ 51 : Remainder = 0

170 ÷ 85 : Remainder = 0

102 ÷ 102 : Remainder = 0

170 ÷ 170 : Remainder = 0

Hence, Factors of 102 are 1, 2, 3, 6, 17, 34, 51, and 102

And, Factors of 170 are 1, 2, 5, 10, 17, 34, 85, and 170

Examples of GCF

Sammy baked 102 chocolate cookies and 170 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 102 and 170.
GCF of 102 and 170 is 34.

A class has 102 boys and 170 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 102 and 170. Hence, GCF of 102 and 170 is 34.

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.

Ram has 102 cans of Pepsi and 170 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 102 and 170. Hence GCF of 102 and 170 is 34. So the number of tables that can be arranged is 34.

Ariel is making ready to eat meals to share with friends. She has 102 bottles of water and 170 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 102 and 170. So the GCF of 102 and 170 is 34.

Mary has 102 blue buttons and 170 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 102 and 170. Hence, the GCF of 102 and 170 or the greatest arrangement is 34.

Kamal is making identical balloon arrangements for a party. He has 102 maroon balloons, and 170 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 102 and 170. So the GCF of 102 and 170 is 34.

Kunal is making baskets full of nuts and dried fruits. He has 102 bags of nuts and 170 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 102 and 170. So the GCF of 102 and 170 is 34.

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 102 bus tickets and 170 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 102 and 170. Hence, GCF of 102 and 170 is 34.