Factors of 1400 in pair are (1, 1400) , (2, 700) , (4, 350) , (5, 280) , (7, 200) , (8, 175) , (10, 140) , (14, 100) , (20, 70) , (25, 56) , (28, 50) and (35, 40)

How to find factors of a number in pair

Steps to find factors of 1400 in pair

Example: Find factors of 1400 in pair

Factor Pair Pair Factorization
1 and 1400 1 x 1400 = 1400
2 and 700 2 x 700 = 1400
4 and 350 4 x 350 = 1400
5 and 280 5 x 280 = 1400
7 and 200 7 x 200 = 1400
8 and 175 8 x 175 = 1400
10 and 140 10 x 140 = 1400
14 and 100 14 x 100 = 1400
20 and 70 20 x 70 = 1400
25 and 56 25 x 56 = 1400
28 and 50 28 x 50 = 1400
35 and 40 35 x 40 = 1400

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 1400. They are called negative pair factors.

Hence, the negative pairs of 1400 would be ( -1 , -1400 ) .

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 1400 are 1 , 2 , 4 , 5 , 7 , 8 , 10 , 14 , 20 , 25 , 28 , 35 , 40 , 50 , 56 , 70 , 100 , 140 , 175 , 200 , 280 , 350 , 700 , 1400. So, factors of 1400 in pair are (1,1400), (2,700), (4,350), (5,280), (7,200), (8,175), (10,140), (14,100), (20,70), (25,56), (28,50), (35,40).

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. 1400 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 1400.
  • Every number is a factor of zero (0), since 1400 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, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700, 1400 are exact divisors of 1400.
  • Factors of 1400 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700, 1400. Each factor divides 1400 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700, 1400 are all less than or equal to 1400.

Steps to find Factors of 1400

  • Step 1. Find all the numbers that would divide 1400 without leaving any remainder. Starting with the number 1 upto 700 (half of 1400). The number 1 and the number itself are always factors of the given number.
    1400 ÷ 1 : Remainder = 0
    1400 ÷ 2 : Remainder = 0
    1400 ÷ 4 : Remainder = 0
    1400 ÷ 5 : Remainder = 0
    1400 ÷ 7 : Remainder = 0
    1400 ÷ 8 : Remainder = 0
    1400 ÷ 10 : Remainder = 0
    1400 ÷ 14 : Remainder = 0
    1400 ÷ 20 : Remainder = 0
    1400 ÷ 25 : Remainder = 0
    1400 ÷ 28 : Remainder = 0
    1400 ÷ 35 : Remainder = 0
    1400 ÷ 40 : Remainder = 0
    1400 ÷ 50 : Remainder = 0
    1400 ÷ 56 : Remainder = 0
    1400 ÷ 70 : Remainder = 0
    1400 ÷ 100 : Remainder = 0
    1400 ÷ 140 : Remainder = 0
    1400 ÷ 175 : Remainder = 0
    1400 ÷ 200 : Remainder = 0
    1400 ÷ 280 : Remainder = 0
    1400 ÷ 350 : Remainder = 0
    1400 ÷ 700 : Remainder = 0
    1400 ÷ 1400 : Remainder = 0

Hence, Factors of 1400 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700, and 1400

Frequently Asked Questions

  • Is 1400 a composite number?

    Yes 1400 is a composite number.

  • Is 1400 a prime number?

    No 1400 is not a prime number.

  • Is 1400 a perfect square?

    No 1400 is not a perfect square.

  • Write five multiples of 1400.

    Five multiples of 1400 are 2800, 4200, 5600, 7000, 8400.

  • Write all odd factors of 1400?

    The factors of 1400 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700, 1400.
    Odd factors of 1400 are 1 , 5 , 7 , 25 , 35 , 175.

Examples of Factors

Ariel has been asked to write all factor pairs of 1400 but she is finding it difficult. Can you help her find out?

Factors of 1400 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700, 1400. So, factors of 1400 in pair are (1,1400), (2,700), (4,350), (5,280), (7,200), (8,175), (10,140), (14,100), (20,70), (25,56), (28,50), (35,40).

Sammy wants to write all the negative factors of 1400 in pair, but don't know how to start. Help Sammy in writing all the factor pairs.

Negative factors of 1400 are -1, -2, -4, -5, -7, -8, -10, -14, -20, -25, -28, -35, -40, -50, -56, -70, -100, -140, -175, -200, -280, -350, -700, -1400. Hence, factors of 1400 in pair are (-1,-1400), (-2,-700), (-4,-350), (-5,-280), (-7,-200), (-8,-175), (-10,-140), (-14,-100), (-20,-70), (-25,-56), (-28,-50), (-35,-40).

Help Deep in writing the positive factors of 1400 in pair and negative factor of 1400 in pair.

Factors of 1400 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700, 1400. Positive factors of 1400 in pair are (1,1400), (2,700), (4,350), (5,280), (7,200), (8,175), (10,140), (14,100), (20,70), (25,56), (28,50), (35,40). Negative factors of 1400 in pair are (-1,-1400), (-2,-700), (-4,-350), (-5,-280), (-7,-200), (-8,-175), (-10,-140), (-14,-100), (-20,-70), (-25,-56), (-28,-50), (-35,-40).

Find the product of all factors of 1400.

Factors of 1400 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700, 1400. So the product of all factors of 1400 would be 1 x 2 x 4 x 5 x 7 x 8 x 10 x 14 x 20 x 25 x 28 x 35 x 40 x 50 x 56 x 70 x 100 x 140 x 175 x 200 x 280 x 350 x 700 x 1400 = 5.669391237529599e+37.

Find the product of all prime factors of 1400.

Factors of 1400 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700, 1400. Prime factors are 2, 2, 2, 5, 5, 7. So, the product of all prime factors of 1400 would be 2 x 2 x 2 x 5 x 5 x 7 = 1400.

Can you help Sammy list the factors of 1400 and also find the factor pairs?

Factors of 1400 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700, 1400.
Factors of 1400 in pair are (1,1400), (2,700), (4,350), (5,280), (7,200), (8,175), (10,140), (14,100), (20,70), (25,56), (28,50), (35,40).

Sammy has 1400 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 1400 blocks in all possible ways to form a rectangle, we need to calculate factors of 1400 in pair. Therefore, factors of 1400 in pair are (1,1400), (2,700), (4,350), (5,280), (7,200), (8,175), (10,140), (14,100), (20,70), (25,56), (28,50), (35,40)