# Factors of 1260 in pair

Factors of 1260 in pair are (1, 1260) , (2, 630) , (3, 420) , (4, 315) , (5, 252) , (6, 210) , (7, 180) , (9, 140) , (10, 126) , (12, 105) , (14, 90) , (15, 84) , (18, 70) , (20, 63) , (21, 60) , (28, 45) , (30, 42) and (35, 36)

#### How to find factors of a number in pair

 1.   Steps to find factors of 1260 in pair 2.   What is factors of a number in pair? 3.   What are Factors? 4.   Frequently Asked Questions 5.   Examples of factors in pair

### Example: Find factors of 1260 in pair

Factor Pair Pair Factorization
1 and 1260 1 x 1260 = 1260
2 and 630 2 x 630 = 1260
3 and 420 3 x 420 = 1260
4 and 315 4 x 315 = 1260
5 and 252 5 x 252 = 1260
6 and 210 6 x 210 = 1260
7 and 180 7 x 180 = 1260
9 and 140 9 x 140 = 1260
10 and 126 10 x 126 = 1260
12 and 105 12 x 105 = 1260
14 and 90 14 x 90 = 1260
15 and 84 15 x 84 = 1260
18 and 70 18 x 70 = 1260
20 and 63 20 x 63 = 1260
21 and 60 21 x 60 = 1260
28 and 45 28 x 45 = 1260
30 and 42 30 x 42 = 1260
35 and 36 35 x 36 = 1260

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 1260. They are called negative pair factors.

Hence, the negative pairs of 1260 would be ( -1 , -1260 ) .

#### Definition of factor pairs?

In mathematics, factor pair are often given as pair of numbers which when multiplied together give the original number. Every natural number is a product of atleast one factor pair. Eg- Factors of 1260 are 1 , 2 , 3 , 4 , 5 , 6 , 7 , 9 , 10 , 12 , 14 , 15 , 18 , 20 , 21 , 28 , 30 , 35 , 36 , 42 , 45 , 60 , 63 , 70 , 84 , 90 , 105 , 126 , 140 , 180 , 210 , 252 , 315 , 420 , 630 , 1260. So, factors of 1260 in pair are (1,1260), (2,630), (3,420), (4,315), (5,252), (6,210), (7,180), (9,140), (10,126), (12,105), (14,90), (15,84), (18,70), (20,63), (21,60), (28,45), (30,42), (35,36).

#### What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

#### Properties of Factors

• Each number is a factor of itself. Eg. 1260 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 1260.
• Every number is a factor of zero (0), since 1260 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, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 60, 63, 70, 84, 90, 105, 126, 140, 180, 210, 252, 315, 420, 630, 1260 are exact divisors of 1260.
• Factors of 1260 are 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 60, 63, 70, 84, 90, 105, 126, 140, 180, 210, 252, 315, 420, 630, 1260. Each factor divides 1260 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 60, 63, 70, 84, 90, 105, 126, 140, 180, 210, 252, 315, 420, 630, 1260 are all less than or equal to 1260.

#### Steps to find Factors of 1260

• Step 1. Find all the numbers that would divide 1260 without leaving any remainder. Starting with the number 1 upto 630 (half of 1260). The number 1 and the number itself are always factors of the given number.
1260 ÷ 1 : Remainder = 0
1260 ÷ 2 : Remainder = 0
1260 ÷ 3 : Remainder = 0
1260 ÷ 4 : Remainder = 0
1260 ÷ 5 : Remainder = 0
1260 ÷ 6 : Remainder = 0
1260 ÷ 7 : Remainder = 0
1260 ÷ 9 : Remainder = 0
1260 ÷ 10 : Remainder = 0
1260 ÷ 12 : Remainder = 0
1260 ÷ 14 : Remainder = 0
1260 ÷ 15 : Remainder = 0
1260 ÷ 18 : Remainder = 0
1260 ÷ 20 : Remainder = 0
1260 ÷ 21 : Remainder = 0
1260 ÷ 28 : Remainder = 0
1260 ÷ 30 : Remainder = 0
1260 ÷ 35 : Remainder = 0
1260 ÷ 36 : Remainder = 0
1260 ÷ 42 : Remainder = 0
1260 ÷ 45 : Remainder = 0
1260 ÷ 60 : Remainder = 0
1260 ÷ 63 : Remainder = 0
1260 ÷ 70 : Remainder = 0
1260 ÷ 84 : Remainder = 0
1260 ÷ 90 : Remainder = 0
1260 ÷ 105 : Remainder = 0
1260 ÷ 126 : Remainder = 0
1260 ÷ 140 : Remainder = 0
1260 ÷ 180 : Remainder = 0
1260 ÷ 210 : Remainder = 0
1260 ÷ 252 : Remainder = 0
1260 ÷ 315 : Remainder = 0
1260 ÷ 420 : Remainder = 0
1260 ÷ 630 : Remainder = 0
1260 ÷ 1260 : Remainder = 0

Hence, Factors of 1260 are 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 60, 63, 70, 84, 90, 105, 126, 140, 180, 210, 252, 315, 420, 630, and 1260

#### Frequently Asked Questions

• Is 1260 a composite number?

Yes 1260 is a composite number.

• Is 1260 a prime number?

No 1260 is not a prime number.

• What is the mean of factors of 1260?

Factors of 1260 are 1 , 2 , 3 , 4 , 5 , 6 , 7 , 9 , 10 , 12 , 14 , 15 , 18 , 20 , 21 , 28 , 30 , 35 , 36 , 42 , 45 , 60 , 63 , 70 , 84 , 90 , 105 , 126 , 140 , 180 , 210 , 252 , 315 , 420 , 630 , 1260. therefore mean of factors of 1260 is (1 + 2 + 3 + 4 + 5 + 6 + 7 + 9 + 10 + 12 + 14 + 15 + 18 + 20 + 21 + 28 + 30 + 35 + 36 + 42 + 45 + 60 + 63 + 70 + 84 + 90 + 105 + 126 + 140 + 180 + 210 + 252 + 315 + 420 + 630 + 1260) / 36 = 121.33.

• 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

Rustom has been assigned the following tasks by the teacher:
- Finding out all positive factors of 1260.
- Writing all prime factors of 1260.
- Writing all the possible factors of 1260 in pair.
Help him in writing all these.

Positive factors of 1260 are 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 60, 63, 70, 84, 90, 105, 126, 140, 180, 210, 252, 315, 420, 630, 1260.
Prime factors of 1260 are 2, 2, 3, 3, 5, 7.
Factors of 1260 in pair are (1,1260), (2,630), (3,420), (4,315), (5,252), (6,210), (7,180), (9,140), (10,126), (12,105), (14,90), (15,84), (18,70), (20,63), (21,60), (28,45), (30,42), (35,36).

What are the pair factors of 1260?

Factors of 1260 are 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 60, 63, 70, 84, 90, 105, 126, 140, 180, 210, 252, 315, 420, 630, 1260. Hence, the factors of 1260 in pair are (1,1260), (2,630), (3,420), (4,315), (5,252), (6,210), (7,180), (9,140), (10,126), (12,105), (14,90), (15,84), (18,70), (20,63), (21,60), (28,45), (30,42), (35,36).

Can you help Sammy list the factors of 1260 and also find the factor pairs?

Factors of 1260 are 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 60, 63, 70, 84, 90, 105, 126, 140, 180, 210, 252, 315, 420, 630, 1260.
Factors of 1260 in pair are (1,1260), (2,630), (3,420), (4,315), (5,252), (6,210), (7,180), (9,140), (10,126), (12,105), (14,90), (15,84), (18,70), (20,63), (21,60), (28,45), (30,42), (35,36).

The area of a rectangle is 1260 square meters. List all the possible combinations possible for length and breadth in which a designer can design out all the combinations.

For the possible combinations possible for length and breadth in which a designer can design out all the rectangles can be calculated by calculating the factors of 1260 in pair. So, the possible combinations (1,1260), (2,630), (3,420), (4,315), (5,252), (6,210), (7,180), (9,140), (10,126), (12,105), (14,90), (15,84), (18,70), (20,63), (21,60), (28,45), (30,42), (35,36).

Help Diji in finding factors of 1260 by Prime Factorization method and then sorting factors of 1260 in pairs.

Prime factorization of 1260 is 2 x 2 x 3 x 3 x 5 x 7. Factors of 1260 in pair can be written as (1,1260), (2,630), (3,420), (4,315), (5,252), (6,210), (7,180), (9,140), (10,126), (12,105), (14,90), (15,84), (18,70), (20,63), (21,60), (28,45), (30,42), (35,36).

Write the smallest prime factor of 1260.

Smallest prime factor of 1260 is 2.

Write the largest prime factor of 1260.

Largest prime factor of 1260 is 7.

Diji wants to write all the negative factors of 1260. Can you help Diji in doing the same?

Negative factors of 1260 are -1, -2, -3, -4, -5, -6, -7, -9, -10, -12, -14, -15, -18, -20, -21, -28, -30, -35, -36, -42, -45, -60, -63, -70, -84, -90, -105, -126, -140, -180, -210, -252, -315, -420, -630, -1260.

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