GCF of 32 and 40 is 8

- Find all the numbers that would divide 32 and 40 without leaving any remainder as explained in factors below.
- Find the greatest common factor from the list of factors for 32 and 40, and read off the answer!

- Factors for
**32: 1, 2, 4, 8, 16, 32** - Factors for
**40: 1, 2, 4, 5, 8, 10, 20, 40**

Hence, GCf of
*32*
and
*40*
is **8**

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 (32, 40).

- The GCF of two or more given numbers cannot be greater than any of the given number. Eg- GCF of 32 and 40 is 8, where 8 is less than both 32 and 40.
- GCF of two consecutive numbers is always 1.
- The product of GCF and LCM of two given numbers is equal to the product of two numbers.
- The GCF of two given numbers where one of them is a prime number is either 1 or the number itself.

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.

- Each number is a factor of itself. Eg. 32 and 40 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 32 and also of 40.
- Every number is a factor of zero (0), since 32 x 0 = 0 and 40 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, 2, 4, 8, 16, 32 are exact divisors of 32 and 1, 2, 4, 5, 8, 10, 20, 40 are exact divisors of 40.
- Factors of 32 are 1, 2, 4, 8, 16, 32. Each factor divides 32 without leaving a remainder.

Simlarly, factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40. Each factor divides 40 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 8, 16, 32 are all less than or equal to 32 and 1, 2, 4, 5, 8, 10, 20, 40 are all less than or equal to 40.

**Step 1.**Find all the numbers that would divide 32 and 40 without leaving any remainder. Starting with the number 1 upto 16 (half of 32) and 1 upto 20 (half of 40). The number 1 and the number itself are always factors of the given number.32 ÷ 1 : Remainder = 040 ÷ 1 : Remainder = 032 ÷ 2 : Remainder = 040 ÷ 2 : Remainder = 032 ÷ 4 : Remainder = 040 ÷ 4 : Remainder = 032 ÷ 8 : Remainder = 040 ÷ 5 : Remainder = 032 ÷ 16 : Remainder = 040 ÷ 8 : Remainder = 032 ÷ 32 : Remainder = 040 ÷ 10 : Remainder = 040 ÷ 20 : Remainder = 040 ÷ 40 : Remainder = 0

Hence, Factors of
*32* are **1, 2, 4, 8, 16, and 32**

And, Factors of
*40* are **1, 2, 4, 5, 8, 10, 20, and 40**

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 32 and 40.

GCF of 32 and 40 is 8.

To find the greatest number of students that could be in each row, we need to find the GCF of 32 and 40. Hence, GCF of 32 and 40 is 8.

GCF and LCM of two numbers can be related as GCF(32, 40) = ( 32 * 40 ) / LCM(32, 40) = 8.

GCF of 32 and 40 is 8.

To find the greatest number of tables that Ram can stock we need to find the GCF of 32 and 40. Hence GCF of 32 and 40 is 8. So the number of tables that can be arranged is 8.

The greatest number of servings Rubel can create would be equal to the GCF of 32 and 40. Thus GCF of 32 and 40 is 8.

The greatest number of boxes Ariel can make would be equal to GCF of 32 and 40. So the GCF of 32 and 40 is 8.

The greatest number of arrangements that he can make if every balloon is used would be equal to GCF of 32 and 40. So the GCF of 32 and 40 is 8.

To make the greatest number of envelopes Abir needs to find out the GCF of 32 and 40. Hence, GCF of 32 and 40 is 8.