What is GCF of 85 and 102?

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GCF of 85 and 102 is 17

How to find GCF of two numbers

Steps to find GCF of 85 and 102

Find all the numbers that would divide 85 and 102 without leaving any remainder as explained in factors below.
Find the greatest common factor from the list of factors for 85 and 102, and read off the answer!

Example: Find gcf of 85 and 102

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

Hence, GCf of 85 and 102 is 17

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 (85, 102).

Properties of GCF

The GCF of two or more given numbers is always less than the given numbers. Eg- GCF of 85 and 102 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.

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, 17, 85 are exact divisors of 85 and 1, 2, 3, 6, 17, 34, 51, 102 are exact divisors of 102.
Every number other than 1 has at least two factors, namely the number itself and 1.
Each number is a factor of itself. Eg. 85 and 102 are factors of themselves respectively.
1 is a factor of every number. Eg. 1 is a factor of 85 and also of 102.

Steps to find Factors of 85 and 102

Step 1. Find all the numbers that would divide 85 and 102 without leaving any remainder. Starting with the number 1 upto 42 (half of 85) and 1 upto 51 (half of 102). The number 1 and the number itself are always factors of the given number.

85 ÷ 1 : Remainder = 0

102 ÷ 1 : Remainder = 0

85 ÷ 5 : Remainder = 0

102 ÷ 2 : Remainder = 0

85 ÷ 17 : Remainder = 0

102 ÷ 3 : Remainder = 0

85 ÷ 85 : Remainder = 0

102 ÷ 6 : Remainder = 0

102 ÷ 17 : Remainder = 0

102 ÷ 34 : Remainder = 0

102 ÷ 51 : Remainder = 0

102 ÷ 102 : Remainder = 0

Hence, Factors of 85 are 1, 5, 17, and 85

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

Examples of GCF

Sammy baked 85 chocolate cookies and 102 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 85 and 102.
GCF of 85 and 102 is 17.

A class has 85 boys and 102 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 85 and 102. Hence, GCF of 85 and 102 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(85, 102) = ( 85 * 102 ) / LCM(85, 102) = 17.

What is the GCF of 85 and 102?

GCF of 85 and 102 is 17.

Mary has 85 blue buttons and 102 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 85 and 102. Hence, the GCF of 85 and 102 or the greatest arrangement is 17.

Kamal is making identical balloon arrangements for a party. He has 85 maroon balloons, and 102 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 85 and 102. So the GCF of 85 and 102 is 17.

Kunal is making baskets full of nuts and dried fruits. He has 85 bags of nuts and 102 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 85 and 102. So the GCF of 85 and 102 is 17.

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 85 bus tickets and 102 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 85 and 102. Hence, GCF of 85 and 102 is 17.