Factors of 1890 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 27, 30, 35, 42, 45, 54, 63, 70, 90, 105, 126, 135, 189, 210, 270, 315, 378, 630, 945, and 1890

How to find factors of a number

1. Steps to find factors of 1890 using Division Method

Example: Find factors of 1890

  • Divide 1890 by 1: 1890 ÷ 1 : Remainder = 0
  • Divide 1890 by 2: 1890 ÷ 2 : Remainder = 0
  • Divide 1890 by 3: 1890 ÷ 3 : Remainder = 0
  • Divide 1890 by 5: 1890 ÷ 5 : Remainder = 0
  • Divide 1890 by 6: 1890 ÷ 6 : Remainder = 0
  • Divide 1890 by 7: 1890 ÷ 7 : Remainder = 0
  • Divide 1890 by 9: 1890 ÷ 9 : Remainder = 0
  • Divide 1890 by 10: 1890 ÷ 10 : Remainder = 0
  • Divide 1890 by 14: 1890 ÷ 14 : Remainder = 0
  • Divide 1890 by 15: 1890 ÷ 15 : Remainder = 0
  • Divide 1890 by 18: 1890 ÷ 18 : Remainder = 0
  • Divide 1890 by 21: 1890 ÷ 21 : Remainder = 0
  • Divide 1890 by 27: 1890 ÷ 27 : Remainder = 0
  • Divide 1890 by 30: 1890 ÷ 30 : Remainder = 0
  • Divide 1890 by 35: 1890 ÷ 35 : Remainder = 0
  • Divide 1890 by 42: 1890 ÷ 42 : Remainder = 0
  • Divide 1890 by 45: 1890 ÷ 45 : Remainder = 0
  • Divide 1890 by 54: 1890 ÷ 54 : Remainder = 0
  • Divide 1890 by 63: 1890 ÷ 63 : Remainder = 0
  • Divide 1890 by 70: 1890 ÷ 70 : Remainder = 0
  • Divide 1890 by 90: 1890 ÷ 90 : Remainder = 0
  • Divide 1890 by 105: 1890 ÷ 105 : Remainder = 0
  • Divide 1890 by 126: 1890 ÷ 126 : Remainder = 0
  • Divide 1890 by 135: 1890 ÷ 135 : Remainder = 0
  • Divide 1890 by 189: 1890 ÷ 189 : Remainder = 0
  • Divide 1890 by 210: 1890 ÷ 210 : Remainder = 0
  • Divide 1890 by 270: 1890 ÷ 270 : Remainder = 0
  • Divide 1890 by 315: 1890 ÷ 315 : Remainder = 0
  • Divide 1890 by 378: 1890 ÷ 378 : Remainder = 0
  • Divide 1890 by 630: 1890 ÷ 630 : Remainder = 0
  • Divide 1890 by 945: 1890 ÷ 945 : Remainder = 0
  • Divide 1890 by 1890: 1890 ÷ 1890 : Remainder = 0

Hence, Factors of 1890 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 27, 30, 35, 42, 45, 54, 63, 70, 90, 105, 126, 135, 189, 210, 270, 315, 378, 630, 945, and 1890

2. Steps to find factors of 1890 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 1890 using the division method, follow these steps:

  • Step 1. Start dividing 1890 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 1890, which is 2. Divide 1890 by 2 to obtain the quotient (945).
    1890 ÷ 2 = 945
  • Step 3. Repeat step 1 with the obtained quotient (945).
    945 ÷ 3 = 315
    315 ÷ 3 = 105
    105 ÷ 3 = 35
    35 ÷ 5 = 7
    7 ÷ 7 = 1

So, the prime factorization of 1890 is, 1890 = 2 x 3 x 3 x 3 x 5 x 7.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1890 as shown below:

So, the prime factorization of 1890 is, 1890 = 2 x 3 x 3 x 3 x 5 x 7.

3. Find factors of 1890 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 1890 would be the two numbers which, when multiplied, give 1890 as the result.

The following table represents the calculation of factors of 1890 in pairs:

Factor Pair Pair Factorization
1 and 1890 1 x 1890 = 1890
2 and 945 2 x 945 = 1890
3 and 630 3 x 630 = 1890
5 and 378 5 x 378 = 1890
6 and 315 6 x 315 = 1890
7 and 270 7 x 270 = 1890
9 and 210 9 x 210 = 1890
10 and 189 10 x 189 = 1890
14 and 135 14 x 135 = 1890
15 and 126 15 x 126 = 1890
18 and 105 18 x 105 = 1890
21 and 90 21 x 90 = 1890
27 and 70 27 x 70 = 1890
30 and 63 30 x 63 = 1890
35 and 54 35 x 54 = 1890
42 and 45 42 x 45 = 1890

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 1890. They are called negative pair factors.

Hence, the negative pairs of 1890 would be ( -1 , -1890 ) , ( -2 , -945 ) , ( -3 , -630 ) , ( -5 , -378 ) , ( -6 , -315 ) , ( -7 , -270 ) , ( -9 , -210 ) , ( -10 , -189 ) , ( -14 , -135 ) , ( -15 , -126 ) , ( -18 , -105 ) , ( -21 , -90 ) , ( -27 , -70 ) , ( -30 , -63 ) , ( -35 , -54 ) and ( -42 , -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. 1890 is a factor of itself.
  • 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, 5, 6, 7, 9, 10, 14, 15, 18, 21, 27, 30, 35, 42, 45, 54, 63, 70, 90, 105, 126, 135, 189, 210, 270, 315, 378, 630, 945, 1890 are exact divisors of 1890.
  • 1 is a factor of every number. Eg. 1 is a factor of 1890.
  • Every number is a factor of zero (0), since 1890 x 0 = 0.

Frequently Asked Questions

  • Which is the smallest prime factor of 1890?

    Smallest prime factor of 1890 is 2.

  • Is 1890 a perfect square?

    No 1890 is not a perfect square.

  • What are five multiples of 1890?

    First five multiples of 1890 are 3780, 5670, 7560, 9450, 11340.

  • What is prime factorization of 1890?

    Prime factorization of 1890 is 2 x 3 x 3 x 3 x 5 x 7.

  • What are factors of 1890?

    Factors of 1890 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 27, 30, 35, 42, 45, 54, 63, 70, 90, 105, 126, 135, 189, 210, 270, 315, 378, 630, 945, 1890.

  • How do you find factors of a negative number? ( eg. -1890 )?

    Factors of -1890 are -1, -2, -3, -5, -6, -7, -9, -10, -14, -15, -18, -21, -27, -30, -35, -42, -45, -54, -63, -70, -90, -105, -126, -135, -189, -210, -270, -315, -378, -630, -945, -1890.

  • Is 1890 a whole number?

    Yes 1890 is a whole number.

  • Which is greatest factor of 1890?

    The greatest factor of 1890 is 945.

  • What are the prime factors of 1890?

    The factors of 1890 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 27, 30, 35, 42, 45, 54, 63, 70, 90, 105, 126, 135, 189, 210, 270, 315, 378, 630, 945, 1890.
    Prime factors of 1890 are 2, 3, 3, 3, 5, 7.

Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 1890. Can you help her?

Prime factors of 1890 are 2, 3, 3, 3, 5, 7.
Hence, the product of prime factors of 210.

Can you help Rubel to find out the product of the even factors of 1890?

Factors of 1890 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 27, 30, 35, 42, 45, 54, 63, 70, 90, 105, 126, 135, 189, 210, 270, 315, 378, 630, 945, 1890.
Even factors of 1890 are 2, 6, 10, 14, 18, 30, 42, 54, 70, 90, 126, 210, 270, 378, 630, 1890.
Hence, product of even factors of 1890 is; 2 x 6 x 10 x 14 x 18 x 30 x 42 x 54 x 70 x 90 x 126 x 210 x 270 x 378 x 630 x 1890 = 4.168064190298125e+28.

Joy wants to calculate mean of all the factors of 1890. Help him in finding the mean of 1890.

Factors of 1890 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 27, 30, 35, 42, 45, 54, 63, 70, 90, 105, 126, 135, 189, 210, 270, 315, 378, 630, 945, 1890.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 1890 is 1 + 2 + 3 + 5 + 6 + 7 + 9 + 10 + 14 + 15 + 18 + 21 + 27 + 30 + 35 + 42 + 45 + 54 + 63 + 70 + 90 + 105 + 126 + 135 + 189 + 210 + 270 + 315 + 378 + 630 + 945 + 1890 = 5760.
Hence, the mean of factors of 1890 is 5760 ÷ 32 = 180.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 1890? Help her in writing all the factors.

Positive factors are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 27, 30, 35, 42, 45, 54, 63, 70, 90, 105, 126, 135, 189, 210, 270, 315, 378, 630, 945, 1890.
Negative factors are -1, -2, -3, -5, -6, -7, -9, -10, -14, -15, -18, -21, -27, -30, -35, -42, -45, -54, -63, -70, -90, -105, -126, -135, -189, -210, -270, -315, -378, -630, -945, -1890.

How many factors are there for 1890?

Factors of 1890 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 27, 30, 35, 42, 45, 54, 63, 70, 90, 105, 126, 135, 189, 210, 270, 315, 378, 630, 945, 1890.
So there are in total 32 factors.

Joey wants to write all the prime factors of 1890 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1890 are 2, 3, 3, 3, 5, 7.
So in exponential form it can be written as 2 x 33 x 5 x 7.

Kevin has been asked to write 31 factor(s) of 1890. Can you predict the answer?

31 factor(s) of 1890 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 27, 30, 35, 42, 45, 54, 63, 70, 90, 105, 126, 135, 189, 210, 270, 315, 378, 630, 945.