GCF of 1024 and 2016 is 32

- Find all the numbers that would divide 1024 and 2016 without leaving any remainder as explained in factors below.
- Find the greatest common factor from the list of factors for 1024 and 2016, and read off the answer!

- Factors for
**1024: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024** - Factors for
**2016: 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 72, 84, 96, 112, 126, 144, 168, 224, 252, 288, 336, 504, 672, 1008, 2016**

Hence, GCf of
*1024*
and
*2016*
is **32**

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 (1024, 2016).

- The GCF of two or more given numbers cannot be greater than any of the given number. Eg- GCF of 1024 and 2016 is 32, where 32 is less than both 1024 and 2016.
- 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 which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.

- Each number is a factor of itself. Eg. 1024 and 2016 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 1024 and also of 2016.
- Every number is a factor of zero (0), since 1024 x 0 = 0 and 2016 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, 64, 128, 256, 512, 1024 are exact divisors of 1024 and 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 72, 84, 96, 112, 126, 144, 168, 224, 252, 288, 336, 504, 672, 1008, 2016 are exact divisors of 2016.
- Factors of 1024 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024. Each factor divides 1024 without leaving a remainder.

Simlarly, factors of 2016 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 72, 84, 96, 112, 126, 144, 168, 224, 252, 288, 336, 504, 672, 1008, 2016. Each factor divides 2016 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 are all less than or equal to 1024 and 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 72, 84, 96, 112, 126, 144, 168, 224, 252, 288, 336, 504, 672, 1008, 2016 are all less than or equal to 2016.

**Step 1.**Find all the numbers that would divide 1024 and 2016 without leaving any remainder. Starting with the number 1 upto 512 (half of 1024) and 1 upto 1008 (half of 2016). The number 1 and the number itself are always factors of the given number.1024 ÷ 1 : Remainder = 02016 ÷ 1 : Remainder = 01024 ÷ 2 : Remainder = 02016 ÷ 2 : Remainder = 01024 ÷ 4 : Remainder = 02016 ÷ 3 : Remainder = 01024 ÷ 8 : Remainder = 02016 ÷ 4 : Remainder = 01024 ÷ 16 : Remainder = 02016 ÷ 6 : Remainder = 01024 ÷ 32 : Remainder = 02016 ÷ 7 : Remainder = 01024 ÷ 64 : Remainder = 02016 ÷ 8 : Remainder = 01024 ÷ 128 : Remainder = 02016 ÷ 9 : Remainder = 01024 ÷ 256 : Remainder = 02016 ÷ 12 : Remainder = 01024 ÷ 512 : Remainder = 02016 ÷ 14 : Remainder = 01024 ÷ 1024 : Remainder = 02016 ÷ 16 : Remainder = 02016 ÷ 18 : Remainder = 02016 ÷ 21 : Remainder = 02016 ÷ 24 : Remainder = 02016 ÷ 28 : Remainder = 02016 ÷ 32 : Remainder = 02016 ÷ 36 : Remainder = 02016 ÷ 42 : Remainder = 02016 ÷ 48 : Remainder = 02016 ÷ 56 : Remainder = 02016 ÷ 63 : Remainder = 02016 ÷ 72 : Remainder = 02016 ÷ 84 : Remainder = 02016 ÷ 96 : Remainder = 02016 ÷ 112 : Remainder = 02016 ÷ 126 : Remainder = 02016 ÷ 144 : Remainder = 02016 ÷ 168 : Remainder = 02016 ÷ 224 : Remainder = 02016 ÷ 252 : Remainder = 02016 ÷ 288 : Remainder = 02016 ÷ 336 : Remainder = 02016 ÷ 504 : Remainder = 02016 ÷ 672 : Remainder = 02016 ÷ 1008 : Remainder = 02016 ÷ 2016 : Remainder = 0

Hence, Factors of
*1024* are **1, 2, 4, 8, 16, 32, 64, 128, 256, 512, and 1024**

And, Factors of
*2016* are **1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 72, 84, 96, 112, 126, 144, 168, 224, 252, 288, 336, 504, 672, 1008, and 2016**

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 1024 and 2016.

GCF of 1024 and 2016 is 32.

To find the greatest number of students that could be in each row, we need to find the GCF of 1024 and 2016. Hence, GCF of 1024 and 2016 is 32.

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(1024, 2016) = ( 1024 * 2016 ) / LCM(1024, 2016) = 32.

GCF of 1024 and 2016 is 32.

The greatest number of boxes Ariel can make would be equal to GCF of 1024 and 2016. So the GCF of 1024 and 2016 is 32.

Greatest possible way in which Mary can arrange them in groups would be GCF of 1024 and 2016. Hence, the GCF of 1024 and 2016 or the greatest arrangement is 32.

The greatest number of arrangements that he can make if every balloon is used would be equal to GCF of 1024 and 2016. So the GCF of 1024 and 2016 is 32.

the greatest number of baskets that Kunal can make would be equal to GCF of 1024 and 2016. So the GCF of 1024 and 2016 is 32.