Factors of 420 in pair are (1, 420) , (2, 210) , (3, 140) , (4, 105) , (5, 84) , (6, 70) , (7, 60) , (10, 42) , (12, 35) , (14, 30) , (15, 28) and (20, 21)

How to find factors of a number in pair

Steps to find factors of 420 in pair

Example: Find factors of 420 in pair

Factor Pair Pair Factorization
1 and 420 1 x 420 = 420
2 and 210 2 x 210 = 420
3 and 140 3 x 140 = 420
4 and 105 4 x 105 = 420
5 and 84 5 x 84 = 420
6 and 70 6 x 70 = 420
7 and 60 7 x 60 = 420
10 and 42 10 x 42 = 420
12 and 35 12 x 35 = 420
14 and 30 14 x 30 = 420
15 and 28 15 x 28 = 420
20 and 21 20 x 21 = 420

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 420. They are called negative pair factors.

Hence, the negative pairs of 420 would be ( -1 , -420 ) .

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 420 are 1 , 2 , 3 , 4 , 5 , 6 , 7 , 10 , 12 , 14 , 15 , 20 , 21 , 28 , 30 , 35 , 42 , 60 , 70 , 84 , 105 , 140 , 210 , 420. So, factors of 420 in pair are (1,420), (2,210), (3,140), (4,105), (5,84), (6,70), (7,60), (10,42), (12,35), (14,30), (15,28), (20,21).

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. 420 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 420.
  • Every number is a factor of zero (0), since 420 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, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420 are exact divisors of 420.
  • Factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420. Each factor divides 420 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, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420 are all less than or equal to 420.

Steps to find Factors of 420

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

Hence, Factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, and 420

Frequently Asked Questions

  • Is 420 a composite number?

    Yes 420 is a composite number.

  • Is 420 a prime number?

    No 420 is not a prime number.

  • What is the mean of factors of 420?

    Factors of 420 are 1 , 2 , 3 , 4 , 5 , 6 , 7 , 10 , 12 , 14 , 15 , 20 , 21 , 28 , 30 , 35 , 42 , 60 , 70 , 84 , 105 , 140 , 210 , 420. therefore mean of factors of 420 is (1 + 2 + 3 + 4 + 5 + 6 + 7 + 10 + 12 + 14 + 15 + 20 + 21 + 28 + 30 + 35 + 42 + 60 + 70 + 84 + 105 + 140 + 210 + 420) / 24 = 56.00.

  • 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

Rustom has been assigned the following tasks by the teacher:
- Finding out all positive factors of 420.
- Writing all prime factors of 420.
- Writing all the possible factors of 420 in pair.
Help him in writing all these.

Positive factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420.
Prime factors of 420 are 2, 2, 3, 5, 7.
Factors of 420 in pair are (1,420), (2,210), (3,140), (4,105), (5,84), (6,70), (7,60), (10,42), (12,35), (14,30), (15,28), (20,21).

What are the pair factors of 420?

Factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420. Hence, the factors of 420 in pair are (1,420), (2,210), (3,140), (4,105), (5,84), (6,70), (7,60), (10,42), (12,35), (14,30), (15,28), (20,21).

Can you help Sammy list the factors of 420 and also find the factor pairs?

Factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420.
Factors of 420 in pair are (1,420), (2,210), (3,140), (4,105), (5,84), (6,70), (7,60), (10,42), (12,35), (14,30), (15,28), (20,21).

The area of a rectangle is 420 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 420 in pair. So, the possible combinations (1,420), (2,210), (3,140), (4,105), (5,84), (6,70), (7,60), (10,42), (12,35), (14,30), (15,28), (20,21).

Help Diji in finding factors of 420 by Prime Factorization method and then sorting factors of 420 in pairs.

Prime factorization of 420 is 2 x 2 x 3 x 5 x 7. Factors of 420 in pair can be written as (1,420), (2,210), (3,140), (4,105), (5,84), (6,70), (7,60), (10,42), (12,35), (14,30), (15,28), (20,21).

Write the smallest prime factor of 420.

Smallest prime factor of 420 is 2.

Write the largest prime factor of 420.

Largest prime factor of 420 is 7.

Diji wants to write all the negative factors of 420. Can you help Diji in doing the same?

Negative factors of 420 are -1, -2, -3, -4, -5, -6, -7, -10, -12, -14, -15, -20, -21, -28, -30, -35, -42, -60, -70, -84, -105, -140, -210, -420.