Factors of 1620 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 81, 90, 108, 135, 162, 180, 270, 324, 405, 540, 810, and 1620

How to find factors of a number

1. Steps to find factors of 1620 using Division Method

Example: Find factors of 1620

  • Divide 1620 by 1: 1620 ÷ 1 : Remainder = 0
  • Divide 1620 by 2: 1620 ÷ 2 : Remainder = 0
  • Divide 1620 by 3: 1620 ÷ 3 : Remainder = 0
  • Divide 1620 by 4: 1620 ÷ 4 : Remainder = 0
  • Divide 1620 by 5: 1620 ÷ 5 : Remainder = 0
  • Divide 1620 by 6: 1620 ÷ 6 : Remainder = 0
  • Divide 1620 by 9: 1620 ÷ 9 : Remainder = 0
  • Divide 1620 by 10: 1620 ÷ 10 : Remainder = 0
  • Divide 1620 by 12: 1620 ÷ 12 : Remainder = 0
  • Divide 1620 by 15: 1620 ÷ 15 : Remainder = 0
  • Divide 1620 by 18: 1620 ÷ 18 : Remainder = 0
  • Divide 1620 by 20: 1620 ÷ 20 : Remainder = 0
  • Divide 1620 by 27: 1620 ÷ 27 : Remainder = 0
  • Divide 1620 by 30: 1620 ÷ 30 : Remainder = 0
  • Divide 1620 by 36: 1620 ÷ 36 : Remainder = 0
  • Divide 1620 by 45: 1620 ÷ 45 : Remainder = 0
  • Divide 1620 by 54: 1620 ÷ 54 : Remainder = 0
  • Divide 1620 by 60: 1620 ÷ 60 : Remainder = 0
  • Divide 1620 by 81: 1620 ÷ 81 : Remainder = 0
  • Divide 1620 by 90: 1620 ÷ 90 : Remainder = 0
  • Divide 1620 by 108: 1620 ÷ 108 : Remainder = 0
  • Divide 1620 by 135: 1620 ÷ 135 : Remainder = 0
  • Divide 1620 by 162: 1620 ÷ 162 : Remainder = 0
  • Divide 1620 by 180: 1620 ÷ 180 : Remainder = 0
  • Divide 1620 by 270: 1620 ÷ 270 : Remainder = 0
  • Divide 1620 by 324: 1620 ÷ 324 : Remainder = 0
  • Divide 1620 by 405: 1620 ÷ 405 : Remainder = 0
  • Divide 1620 by 540: 1620 ÷ 540 : Remainder = 0
  • Divide 1620 by 810: 1620 ÷ 810 : Remainder = 0
  • Divide 1620 by 1620: 1620 ÷ 1620 : Remainder = 0

Hence, Factors of 1620 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 81, 90, 108, 135, 162, 180, 270, 324, 405, 540, 810, and 1620

2. Steps to find factors of 1620 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

Method 1: Division Method

To find the primefactors of 1620 using the division method, follow these steps:

  • Step 1. Start dividing 1620 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
  • Step 2. After finding the smallest prime factor of the number 1620, which is 2. Divide 1620 by 2 to obtain the quotient (810).
    1620 ÷ 2 = 810
  • Step 3. Repeat step 1 with the obtained quotient (810).
    810 ÷ 2 = 405
    405 ÷ 3 = 135
    135 ÷ 3 = 45
    45 ÷ 3 = 15
    15 ÷ 3 = 5
    5 ÷ 5 = 1

So, the prime factorization of 1620 is, 1620 = 2 x 2 x 3 x 3 x 3 x 3 x 5.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1620 as shown below:

So, the prime factorization of 1620 is, 1620 = 2 x 2 x 3 x 3 x 3 x 3 x 5.

3. Find factors of 1620 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 1620 would be the two numbers which, when multiplied, give 1620 as the result.

The following table represents the calculation of factors of 1620 in pairs:

Factor Pair Pair Factorization
1 and 1620 1 x 1620 = 1620
2 and 810 2 x 810 = 1620
3 and 540 3 x 540 = 1620
4 and 405 4 x 405 = 1620
5 and 324 5 x 324 = 1620
6 and 270 6 x 270 = 1620
9 and 180 9 x 180 = 1620
10 and 162 10 x 162 = 1620
12 and 135 12 x 135 = 1620
15 and 108 15 x 108 = 1620
18 and 90 18 x 90 = 1620
20 and 81 20 x 81 = 1620
27 and 60 27 x 60 = 1620
30 and 54 30 x 54 = 1620
36 and 45 36 x 45 = 1620

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 1620. They are called negative pair factors.

Hence, the negative pairs of 1620 would be ( -1 , -1620 ) , ( -2 , -810 ) , ( -3 , -540 ) , ( -4 , -405 ) , ( -5 , -324 ) , ( -6 , -270 ) , ( -9 , -180 ) , ( -10 , -162 ) , ( -12 , -135 ) , ( -15 , -108 ) , ( -18 , -90 ) , ( -20 , -81 ) , ( -27 , -60 ) , ( -30 , -54 ) and ( -36 , -45 ) .

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. 1620 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 1620.
  • Every number is a factor of zero (0), since 1620 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, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 81, 90, 108, 135, 162, 180, 270, 324, 405, 540, 810, 1620 are exact divisors of 1620.
  • Factors of 1620 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 81, 90, 108, 135, 162, 180, 270, 324, 405, 540, 810, 1620. Each factor divides 1620 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 81, 90, 108, 135, 162, 180, 270, 324, 405, 540, 810, 1620 are all less than or equal to 1620.

Frequently Asked Questions

  • Which is the smallest prime factor of 1620?

    Smallest prime factor of 1620 is 2.

  • Is 1620 a perfect square?

    No 1620 is not a perfect square.

  • What are five multiples of 1620?

    First five multiples of 1620 are 3240, 4860, 6480, 8100, 9720.

  • What is prime factorization of 1620?

    Prime factorization of 1620 is 2 x 2 x 3 x 3 x 3 x 3 x 5.

  • What are factors of 1620?

    Factors of 1620 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 81, 90, 108, 135, 162, 180, 270, 324, 405, 540, 810, 1620.

  • How do you find factors of a negative number? ( eg. -1620 )?

    Factors of -1620 are -1, -2, -3, -4, -5, -6, -9, -10, -12, -15, -18, -20, -27, -30, -36, -45, -54, -60, -81, -90, -108, -135, -162, -180, -270, -324, -405, -540, -810, -1620.

  • Is 1620 a whole number?

    Yes 1620 is a whole number.

  • Which is greatest factor of 1620?

    The greatest factor of 1620 is 810.

  • What are the prime factors of 1620?

    The factors of 1620 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 81, 90, 108, 135, 162, 180, 270, 324, 405, 540, 810, 1620.
    Prime factors of 1620 are 2, 2, 3, 3, 3, 3, 5.

Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 1620. Can you help her?

Prime factors of 1620 are 2, 2, 3, 3, 3, 3, 5.
Hence, the product of prime factors of 30.

Can you help Rubel to find out the product of the even factors of 1620?

Factors of 1620 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 81, 90, 108, 135, 162, 180, 270, 324, 405, 540, 810, 1620.
Even factors of 1620 are 2, 4, 6, 10, 12, 18, 20, 30, 36, 54, 60, 90, 108, 162, 180, 270, 324, 540, 810, 1620.
Hence, product of even factors of 1620 is; 2 x 4 x 6 x 10 x 12 x 18 x 20 x 30 x 36 x 54 x 60 x 90 x 108 x 162 x 180 x 270 x 324 x 540 x 810 x 1620 = 1.2748236216396079e+35.

Joy wants to calculate mean of all the factors of 1620. Help him in finding the mean of 1620.

Factors of 1620 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 81, 90, 108, 135, 162, 180, 270, 324, 405, 540, 810, 1620.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 1620 is 1 + 2 + 3 + 4 + 5 + 6 + 9 + 10 + 12 + 15 + 18 + 20 + 27 + 30 + 36 + 45 + 54 + 60 + 81 + 90 + 108 + 135 + 162 + 180 + 270 + 324 + 405 + 540 + 810 + 1620 = 5082.
Hence, the mean of factors of 1620 is 5082 ÷ 30 = 169.40.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 1620? Help her in writing all the factors.

Positive factors are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 81, 90, 108, 135, 162, 180, 270, 324, 405, 540, 810, 1620.
Negative factors are -1, -2, -3, -4, -5, -6, -9, -10, -12, -15, -18, -20, -27, -30, -36, -45, -54, -60, -81, -90, -108, -135, -162, -180, -270, -324, -405, -540, -810, -1620.

How many factors are there for 1620?

Factors of 1620 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 81, 90, 108, 135, 162, 180, 270, 324, 405, 540, 810, 1620.
So there are in total 30 factors.

Joey wants to write all the prime factors of 1620 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1620 are 2, 2, 3, 3, 3, 3, 5.
So in exponential form it can be written as 22 x 34 x 5.

Kevin has been asked to write 29 factor(s) of 1620. Can you predict the answer?

29 factor(s) of 1620 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 81, 90, 108, 135, 162, 180, 270, 324, 405, 540, 810.