Factors of 1764 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 49, 63, 84, 98, 126, 147, 196, 252, 294, 441, 588, 882, and 1764

How to find factors of a number

1. Steps to find factors of 1764 using Division Method

Example: Find factors of 1764

  • Divide 1764 by 1: 1764 ÷ 1 : Remainder = 0
  • Divide 1764 by 2: 1764 ÷ 2 : Remainder = 0
  • Divide 1764 by 3: 1764 ÷ 3 : Remainder = 0
  • Divide 1764 by 4: 1764 ÷ 4 : Remainder = 0
  • Divide 1764 by 6: 1764 ÷ 6 : Remainder = 0
  • Divide 1764 by 7: 1764 ÷ 7 : Remainder = 0
  • Divide 1764 by 9: 1764 ÷ 9 : Remainder = 0
  • Divide 1764 by 12: 1764 ÷ 12 : Remainder = 0
  • Divide 1764 by 14: 1764 ÷ 14 : Remainder = 0
  • Divide 1764 by 18: 1764 ÷ 18 : Remainder = 0
  • Divide 1764 by 21: 1764 ÷ 21 : Remainder = 0
  • Divide 1764 by 28: 1764 ÷ 28 : Remainder = 0
  • Divide 1764 by 36: 1764 ÷ 36 : Remainder = 0
  • Divide 1764 by 42: 1764 ÷ 42 : Remainder = 0
  • Divide 1764 by 49: 1764 ÷ 49 : Remainder = 0
  • Divide 1764 by 63: 1764 ÷ 63 : Remainder = 0
  • Divide 1764 by 84: 1764 ÷ 84 : Remainder = 0
  • Divide 1764 by 98: 1764 ÷ 98 : Remainder = 0
  • Divide 1764 by 126: 1764 ÷ 126 : Remainder = 0
  • Divide 1764 by 147: 1764 ÷ 147 : Remainder = 0
  • Divide 1764 by 196: 1764 ÷ 196 : Remainder = 0
  • Divide 1764 by 252: 1764 ÷ 252 : Remainder = 0
  • Divide 1764 by 294: 1764 ÷ 294 : Remainder = 0
  • Divide 1764 by 441: 1764 ÷ 441 : Remainder = 0
  • Divide 1764 by 588: 1764 ÷ 588 : Remainder = 0
  • Divide 1764 by 882: 1764 ÷ 882 : Remainder = 0
  • Divide 1764 by 1764: 1764 ÷ 1764 : Remainder = 0

Hence, Factors of 1764 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 49, 63, 84, 98, 126, 147, 196, 252, 294, 441, 588, 882, and 1764

2. Steps to find factors of 1764 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 1764 using the division method, follow these steps:

  • Step 1. Start dividing 1764 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 1764, which is 2. Divide 1764 by 2 to obtain the quotient (882).
    1764 ÷ 2 = 882
  • Step 3. Repeat step 1 with the obtained quotient (882).
    882 ÷ 2 = 441
    441 ÷ 3 = 147
    147 ÷ 3 = 49
    49 ÷ 7 = 7
    7 ÷ 7 = 1

So, the prime factorization of 1764 is, 1764 = 2 x 2 x 3 x 3 x 7 x 7.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1764 as shown below:

So, the prime factorization of 1764 is, 1764 = 2 x 2 x 3 x 3 x 7 x 7.

3. Find factors of 1764 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 1764 would be the two numbers which, when multiplied, give 1764 as the result.

The following table represents the calculation of factors of 1764 in pairs:

Factor Pair Pair Factorization
1 and 1764 1 x 1764 = 1764
2 and 882 2 x 882 = 1764
3 and 588 3 x 588 = 1764
4 and 441 4 x 441 = 1764
6 and 294 6 x 294 = 1764
7 and 252 7 x 252 = 1764
9 and 196 9 x 196 = 1764
12 and 147 12 x 147 = 1764
14 and 126 14 x 126 = 1764
18 and 98 18 x 98 = 1764
21 and 84 21 x 84 = 1764
28 and 63 28 x 63 = 1764
36 and 49 36 x 49 = 1764
42 and 42 42 x 42 = 1764

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 1764. They are called negative pair factors.

Hence, the negative pairs of 1764 would be ( -1 , -1764 ) , ( -2 , -882 ) , ( -3 , -588 ) , ( -4 , -441 ) , ( -6 , -294 ) , ( -7 , -252 ) , ( -9 , -196 ) , ( -12 , -147 ) , ( -14 , -126 ) , ( -18 , -98 ) , ( -21 , -84 ) , ( -28 , -63 ) , ( -36 , -49 ) and ( -42 , -42 ) .

How can we define factors?

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

Properties of factors

  • Each number is a factor of itself. Eg. 1764 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 1764.
  • Every number is a factor of zero (0), since 1764 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, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 49, 63, 84, 98, 126, 147, 196, 252, 294, 441, 588, 882, 1764 are exact divisors of 1764.
  • Factors of 1764 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 49, 63, 84, 98, 126, 147, 196, 252, 294, 441, 588, 882, 1764. Each factor divides 1764 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 49, 63, 84, 98, 126, 147, 196, 252, 294, 441, 588, 882, 1764 are all less than or equal to 1764.

Frequently Asked Questions

  • Which is the smallest prime factor of 1764?

    Smallest prime factor of 1764 is 2.

  • Is 1764 a perfect square?

    Yes 1764 is a perfect square.

  • What are five multiples of 1764?

    First five multiples of 1764 are 3528, 5292, 7056, 8820, 10584.

  • What is prime factorization of 1764?

    Prime factorization of 1764 is 2 x 2 x 3 x 3 x 7 x 7.

  • What are factors of 1764?

    Factors of 1764 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 49, 63, 84, 98, 126, 147, 196, 252, 294, 441, 588, 882, 1764.

  • How do you find factors of a negative number? ( eg. -1764 )?

    Factors of -1764 are -1, -2, -3, -4, -6, -7, -9, -12, -14, -18, -21, -28, -36, -42, -49, -63, -84, -98, -126, -147, -196, -252, -294, -441, -588, -882, -1764.

  • Is 1764 a whole number?

    Yes 1764 is a whole number.

  • Which is greatest factor of 1764?

    The greatest factor of 1764 is 882.

  • What are the prime factors of 1764?

    The factors of 1764 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 49, 63, 84, 98, 126, 147, 196, 252, 294, 441, 588, 882, 1764.
    Prime factors of 1764 are 2, 2, 3, 3, 7, 7.

Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 1764. Can you help her?

Prime factors of 1764 are 2, 2, 3, 3, 7, 7.
Hence, the product of prime factors of 42.

Can you help Rubel to find out the product of the even factors of 1764?

Factors of 1764 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 49, 63, 84, 98, 126, 147, 196, 252, 294, 441, 588, 882, 1764.
Even factors of 1764 are 2, 4, 6, 12, 14, 18, 28, 36, 42, 84, 98, 126, 196, 252, 294, 588, 882, 1764.
Hence, product of even factors of 1764 is; 2 x 4 x 6 x 12 x 14 x 18 x 28 x 36 x 42 x 84 x 98 x 126 x 196 x 252 x 294 x 588 x 882 x 1764 = 8.467538659432682e+31.

Joy wants to calculate mean of all the factors of 1764. Help him in finding the mean of 1764.

Factors of 1764 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 49, 63, 84, 98, 126, 147, 196, 252, 294, 441, 588, 882, 1764.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 1764 is 1 + 2 + 3 + 4 + 6 + 7 + 9 + 12 + 14 + 18 + 21 + 28 + 36 + 42 + 49 + 63 + 84 + 98 + 126 + 147 + 196 + 252 + 294 + 441 + 588 + 882 + 1764 = 5187.
Hence, the mean of factors of 1764 is 5187 ÷ 27 = 192.11.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 1764? Help her in writing all the factors.

Positive factors are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 49, 63, 84, 98, 126, 147, 196, 252, 294, 441, 588, 882, 1764.
Negative factors are -1, -2, -3, -4, -6, -7, -9, -12, -14, -18, -21, -28, -36, -42, -49, -63, -84, -98, -126, -147, -196, -252, -294, -441, -588, -882, -1764.

How many factors are there for 1764?

Factors of 1764 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 49, 63, 84, 98, 126, 147, 196, 252, 294, 441, 588, 882, 1764.
So there are in total 27 factors.

Joey wants to write all the prime factors of 1764 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1764 are 2, 2, 3, 3, 7, 7.
So in exponential form it can be written as 22 x 32 x 72.

Kevin has been asked to write 26 factor(s) of 1764. Can you predict the answer?

26 factor(s) of 1764 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 49, 63, 84, 98, 126, 147, 196, 252, 294, 441, 588, 882.