Factors of 1008 in pair

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

How to find factors of a number in pair

Steps to find factors of 1008 in pair

Find all the numbers that would divide 1008 without leaving any remainder. Starting with the number 1 upto 504 (half of 1008). The number 1 and the number itself are always factors of the given number.
Pair the factors so that their product is 1008, and read off the answer!

Example: Find factors of 1008 in pair

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

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 1008. They are called negative pair factors.

Hence, the negative pairs of 1008 would be ( -1 , -1008 ) .

What does factor pairs in mathematics mean?

In mathematics, factor pair of a number are all those possible combination which when multiplied together give the original number in return. Every natural number is a product of atleast one factor pair. Eg- Factors of 1008 are 1 , 2 , 3 , 4 , 6 , 7 , 8 , 9 , 12 , 14 , 16 , 18 , 21 , 24 , 28 , 36 , 42 , 48 , 56 , 63 , 72 , 84 , 112 , 126 , 144 , 168 , 252 , 336 , 504 , 1008. So, factors of 1008 in pair are (1,1008), (2,504), (3,336), (4,252), (6,168), (7,144), (8,126), (9,112), (12,84), (14,72), (16,63), (18,56), (21,48), (24,42), (28,36).

What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

Properties of Factors

Each number is a factor of itself. Eg. 1008 is a factor of itself.
1 is a factor of every number. Eg. 1 is a factor of 1008.
Every number is a factor of zero (0), since 1008 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, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, 1008 are exact divisors of 1008.
Factors of 1008 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, 1008. Each factor divides 1008 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, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, 1008 are all less than or equal to 1008.

Steps to find Factors of 1008

Step 1. Find all the numbers that would divide 1008 without leaving any remainder. Starting with the number 1 upto 504 (half of 1008). The number 1 and the number itself are always factors of the given number.

1008 ÷ 1 : Remainder = 0

1008 ÷ 2 : Remainder = 0

1008 ÷ 3 : Remainder = 0

1008 ÷ 4 : Remainder = 0

1008 ÷ 6 : Remainder = 0

1008 ÷ 7 : Remainder = 0

1008 ÷ 8 : Remainder = 0

1008 ÷ 9 : Remainder = 0

1008 ÷ 12 : Remainder = 0

1008 ÷ 14 : Remainder = 0

1008 ÷ 16 : Remainder = 0

1008 ÷ 18 : Remainder = 0

1008 ÷ 21 : Remainder = 0

1008 ÷ 24 : Remainder = 0

1008 ÷ 28 : Remainder = 0

1008 ÷ 36 : Remainder = 0

1008 ÷ 42 : Remainder = 0

1008 ÷ 48 : Remainder = 0

1008 ÷ 56 : Remainder = 0

1008 ÷ 63 : Remainder = 0

1008 ÷ 72 : Remainder = 0

1008 ÷ 84 : Remainder = 0

1008 ÷ 112 : Remainder = 0

1008 ÷ 126 : Remainder = 0

1008 ÷ 144 : Remainder = 0

1008 ÷ 168 : Remainder = 0

1008 ÷ 252 : Remainder = 0

1008 ÷ 336 : Remainder = 0

1008 ÷ 504 : Remainder = 0

1008 ÷ 1008 : Remainder = 0

Hence, Factors of 1008 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, and 1008

Frequently Asked Questions

Is 1008 a composite number?
Yes 1008 is a composite number.
Is 1008 a prime number?
No 1008 is not a prime number.
What is the mean of factors of 1008?
Factors of 1008 are 1 , 2 , 3 , 4 , 6 , 7 , 8 , 9 , 12 , 14 , 16 , 18 , 21 , 24 , 28 , 36 , 42 , 48 , 56 , 63 , 72 , 84 , 112 , 126 , 144 , 168 , 252 , 336 , 504 , 1008. therefore mean of factors of 1008 is (1 + 2 + 3 + 4 + 6 + 7 + 8 + 9 + 12 + 14 + 16 + 18 + 21 + 24 + 28 + 36 + 42 + 48 + 56 + 63 + 72 + 84 + 112 + 126 + 144 + 168 + 252 + 336 + 504 + 1008) / 30 = 107.47.
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 1008 but she is finding it difficult. Can you help her find out?

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

Sammy wants to write all the negative factors of 1008 in pair, but don't know how to start. Help Sammy in writing all the factor pairs.

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

Help Deep in writing the positive factors of 1008 in pair and negative factor of 1008 in pair.

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

Find the product of all factors of 1008.

Factors of 1008 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, 1008. So the product of all factors of 1008 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 36 x 42 x 48 x 56 x 63 x 72 x 84 x 112 x 126 x 144 x 168 x 252 x 336 x 504 x 1008 = 1.1269586507679386e+45.

Find the product of all prime factors of 1008.

Factors of 1008 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, 1008. Prime factors are 2, 2, 2, 2, 3, 3, 7. So, the product of all prime factors of 1008 would be 2 x 2 x 2 x 2 x 3 x 3 x 7 = 1008.

Can you help Sammy list the factors of 1008 and also find the factor pairs?

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

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