GCF of 27 and 36 is 9

- Find all the numbers that would divide 27 and 36 without leaving any remainder as explained in factors below.
- Find the greatest common factor from the list of factors for 27 and 36, and read off the answer!

- Factors for
**27: 1, 3, 9, 27** - Factors for
**36: 1, 2, 3, 4, 6, 9, 12, 18, 36**

Hence, GCf of
*27*
and
*36*
is **9**

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 (27, 36).

- The GCF of two given numbers where one of them is a prime number is either 1 or the number itself.
- GCF of two consecutive numbers is always 1.
- Given two numbers 27 and 36, such that GCF is 9 where 9 will always be less than 27 and 36.
- Product of two numbers is always equal to the product of their GCF and LCM.

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.

- Every number is a factor of zero (0), since 27 x 0 = 0 and 36 x 0 = 0.
- 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, 3, 9, 27 are exact divisors of 27 and 1, 2, 3, 4, 6, 9, 12, 18, 36 are exact divisors of 36.
- Factors of 27 are 1, 3, 9, 27. Each factor divides 27 without leaving a remainder.

Simlarly, factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. Each factor divides 36 without leaving a remainder.

**Step 1.**Find all the numbers that would divide 27 and 36 without leaving any remainder. Starting with the number 1 upto 13 (half of 27) and 1 upto 18 (half of 36). The number 1 and the number itself are always factors of the given number.27 ÷ 1 : Remainder = 036 ÷ 1 : Remainder = 027 ÷ 3 : Remainder = 036 ÷ 2 : Remainder = 027 ÷ 9 : Remainder = 036 ÷ 3 : Remainder = 027 ÷ 27 : Remainder = 036 ÷ 4 : Remainder = 036 ÷ 6 : Remainder = 036 ÷ 9 : Remainder = 036 ÷ 12 : Remainder = 036 ÷ 18 : Remainder = 036 ÷ 36 : Remainder = 0

Hence, Factors of
*27* are **1, 3, 9, and 27**

And, Factors of
*36* are **1, 2, 3, 4, 6, 9, 12, 18, and 36**

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 27 and 36.

GCF of 27 and 36 is 9.

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.

GCF and LCM of two numbers can be related as GCF(27, 36) = ( 27 * 36 ) / LCM(27, 36) = 9.

GCF of 27 and 36 is 9.

To find the greatest number of tables that Ram can stock we need to find the GCF of 27 and 36. Hence GCF of 27 and 36 is 9. So the number of tables that can be arranged is 9.

The greatest number of servings Rubel can create would be equal to the GCF of 27 and 36. Thus GCF of 27 and 36 is 9.

The greatest number of boxes Ariel can make would be equal to GCF of 27 and 36. So the GCF of 27 and 36 is 9.

Greatest possible way in which Mary can arrange them in groups would be GCF of 27 and 36. Hence, the GCF of 27 and 36 or the greatest arrangement is 9.

The greatest number of arrangements that he can make if every balloon is used would be equal to GCF of 27 and 36. So the GCF of 27 and 36 is 9.