What is GCF of 34 and 102?


Steps to find GCF of 34 and 102

Example: Find gcf of 34 and 102

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

Hence, GCf of 34 and 102 is 34

How do you explain GCF in mathematics?

GCF or greatest common factor of two or more numbers is defined as largest possible number or integer which is the factor of all given number or in other words we can say that largest possible common number which completely divides the given numbers. GCF of two numbers can be represented as GCF (34, 102).

Properties of GCF

  • Given two numbers 34 and 102, such that GCF is 34 where 34 will always be less than 34 and 102.
  • 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 can we define factors?

In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.

Properties of Factors

  • Each number is a factor of itself. Eg. 34 and 102 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, 17, 34 are exact divisors of 34 and 1, 2, 3, 6, 17, 34, 51, 102 are exact divisors of 102.
  • 1 is a factor of every number. Eg. 1 is a factor of 34 and also of 102.
  • Every number is a factor of zero (0), since 34 x 0 = 0 and 102 x 0 = 0.

Steps to find Factors of 34 and 102

  • Step 1. Find all the numbers that would divide 34 and 102 without leaving any remainder. Starting with the number 1 upto 17 (half of 34) and 1 upto 51 (half of 102). The number 1 and the number itself are always factors of the given number.
    34 ÷ 1 : Remainder = 0
    102 ÷ 1 : Remainder = 0
    34 ÷ 2 : Remainder = 0
    102 ÷ 2 : Remainder = 0
    34 ÷ 17 : Remainder = 0
    102 ÷ 3 : Remainder = 0
    34 ÷ 34 : 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 34 are 1, 2, 17, and 34

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

Examples of GCF

Sammy baked 34 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 34 and 102.
GCF of 34 and 102 is 34.

A class has 34 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 34 and 102. Hence, GCF of 34 and 102 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.

What is the relation between LCM and GCF (Greatest Common Factor)?

GCF and LCM of two numbers can be related as GCF(34, 102) = ( 34 * 102 ) / LCM(34, 102) = 34.

What is the GCF of 34 and 102?

GCF of 34 and 102 is 34.

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

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

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

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