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

How to find factors of a number in pair

Steps to find factors of 2016 in pair

Example: Find factors of 2016 in pair

Factor Pair Pair Factorization
1 and 2016 1 x 2016 = 2016
2 and 1008 2 x 1008 = 2016
3 and 672 3 x 672 = 2016
4 and 504 4 x 504 = 2016
6 and 336 6 x 336 = 2016
7 and 288 7 x 288 = 2016
8 and 252 8 x 252 = 2016
9 and 224 9 x 224 = 2016
12 and 168 12 x 168 = 2016
14 and 144 14 x 144 = 2016
16 and 126 16 x 126 = 2016
18 and 112 18 x 112 = 2016
21 and 96 21 x 96 = 2016
24 and 84 24 x 84 = 2016
28 and 72 28 x 72 = 2016
32 and 63 32 x 63 = 2016
36 and 56 36 x 56 = 2016
42 and 48 42 x 48 = 2016

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 2016. They are called negative pair factors.

Hence, the negative pairs of 2016 would be ( -1 , -2016 ) .

Introduction to factor pairs

Factor pair in mathematics is defined as all factors of a given number which when written in pair and multiplied gives the original number. Every natural number is a product of atleast one factor pair. Eg- 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. So, factors of 2016 in pair are (1,2016), (2,1008), (3,672), (4,504), (6,336), (7,288), (8,252), (9,224), (12,168), (14,144), (16,126), (18,112), (21,96), (24,84), (28,72), (32,63), (36,56), (42,48).

How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

Properties of Factors

  • Each number is a factor of itself. Eg. 2016 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 2016.
  • Every number is a factor of zero (0), since 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, 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 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, 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.

Steps to find Factors of 2016

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

Hence, 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

Frequently Asked Questions

  • Is 2016 a composite number?

    Yes 2016 is a composite number.

  • Is 2016 a prime number?

    No 2016 is not a prime number.

  • What is the mean of factors of 2016?

    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. therefore mean of factors of 2016 is (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) / 36 = 182.00.

  • What do you mean by proper divisors?

    A number x is said to be the proper divisor of y if it divides y completely, given that x is smaller than y.

  • What do you mean by improper divisors?

    An improper divisor of a number is the number itself apart from this any divisor of a given number is a proper divisor.

Examples of Factors

Ariel has been asked to write all factor pairs of 2016 but she is finding it difficult. Can you help her find out?

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. So, factors of 2016 in pair are (1,2016), (2,1008), (3,672), (4,504), (6,336), (7,288), (8,252), (9,224), (12,168), (14,144), (16,126), (18,112), (21,96), (24,84), (28,72), (32,63), (36,56), (42,48).

Sammy wants to write all the negative factors of 2016 in pair, but don't know how to start. Help Sammy in writing all the factor pairs.

Negative 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. Hence, factors of 2016 in pair are (-1,-2016), (-2,-1008), (-3,-672), (-4,-504), (-6,-336), (-7,-288), (-8,-252), (-9,-224), (-12,-168), (-14,-144), (-16,-126), (-18,-112), (-21,-96), (-24,-84), (-28,-72), (-32,-63), (-36,-56), (-42,-48).

Help Deep in writing the positive factors of 2016 in pair and negative factor of 2016 in pair.

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. Positive factors of 2016 in pair are (1,2016), (2,1008), (3,672), (4,504), (6,336), (7,288), (8,252), (9,224), (12,168), (14,144), (16,126), (18,112), (21,96), (24,84), (28,72), (32,63), (36,56), (42,48). Negative factors of 2016 in pair are (-1,-2016), (-2,-1008), (-3,-672), (-4,-504), (-6,-336), (-7,-288), (-8,-252), (-9,-224), (-12,-168), (-14,-144), (-16,-126), (-18,-112), (-21,-96), (-24,-84), (-28,-72), (-32,-63), (-36,-56), (-42,-48).

Find the product of all factors of 2016.

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. So the product of all factors of 2016 would be 1 x 2 x 3 x 4 x 6 x 7 x 8 x 9 x 12 x 14 x 16 x 18 x 21 x 24 x 28 x 32 x 36 x 42 x 48 x 56 x 63 x 72 x 84 x 96 x 112 x 126 x 144 x 168 x 224 x 252 x 288 x 336 x 504 x 672 x 1008 x 2016 = 3.025725322559871e+59.

Find the product of all prime factors of 2016.

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. Prime factors are 2, 2, 2, 2, 2, 3, 3, 7. So, the product of all prime factors of 2016 would be 2 x 2 x 2 x 2 x 2 x 3 x 3 x 7 = 2016.

Can you help Sammy list the factors of 2016 and also find the factor pairs?

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

Sammy has 2016 blocks and he wants to arrange them in all possible ways to form a rectangle but he doesn't know the technique for doing that, help Sammy in arrangements.

To arrange 2016 blocks in all possible ways to form a rectangle, we need to calculate factors of 2016 in pair. Therefore, factors of 2016 in pair are (1,2016), (2,1008), (3,672), (4,504), (6,336), (7,288), (8,252), (9,224), (12,168), (14,144), (16,126), (18,112), (21,96), (24,84), (28,72), (32,63), (36,56), (42,48)