The art teacher has 36 small sticks and 60 pipe cleaners for art projects. He wants to make kits for all the students using all the sticks and pipe cleaners. All the kits must be alike. He wants to make as many kits as possible. What is the greatest number of kits he can make. A) 8 kits

B) 9 kits

C) 12 kits

D) 36 kits

The greatest number of kits he can make is 12 kits

Step-by-step explanation:

The greatest common divisor or GCD is called the greatest number that divides exactly two or more numbers at the same time.

The greatest common divisor is usually expressed as  GCD(a,b), where a and b are numbers.

Being the divisor of a number is the value that divides the number into exact parts, that is, that the remainder is zero, one way to calculate the GCD is to determine all the divisors of each number, and from these point out the common divisors, of which the major divisor will be the GCD of those numbers. In this case:

Divisors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.

Divisors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.

The common divisors of 36 and 60 are 1, 2, 3, 4, 6 and 12, of which the greatest is 12. So GCD(36,60)=12

Another way to calculate the GCD is through prime factorization, which always starts with the smallest divisible number of the number being analyzed. In this case:

The decomposition of 36 is: 2*2*3*3 = 2²*3²

The decomposition of 60 is: 2*2*3*5= 2²*3*5

Now the common factors with the lowest exponent are chosen and multiplied. The result obtained is the GCD. In this case, the common factors of 36 and 60 are: 2² and 3 and their multiplication gives: 2²*3= 12. So GCD(36,60)=12

The greatest number of kits he can make is 12 kits