Factors of 3528 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 49, 56, 63, 72, 84, 98, 126, 147, 168, 196, 252, 294, 392, 441, 504, 588, 882, 1176, 1764, and 3528

How to find factors of a number

1. Steps to find factors of 3528 using Division Method

Example: Find factors of 3528

  • Divide 3528 by 1: 3528 ÷ 1 : Remainder = 0
  • Divide 3528 by 2: 3528 ÷ 2 : Remainder = 0
  • Divide 3528 by 3: 3528 ÷ 3 : Remainder = 0
  • Divide 3528 by 4: 3528 ÷ 4 : Remainder = 0
  • Divide 3528 by 6: 3528 ÷ 6 : Remainder = 0
  • Divide 3528 by 7: 3528 ÷ 7 : Remainder = 0
  • Divide 3528 by 8: 3528 ÷ 8 : Remainder = 0
  • Divide 3528 by 9: 3528 ÷ 9 : Remainder = 0
  • Divide 3528 by 12: 3528 ÷ 12 : Remainder = 0
  • Divide 3528 by 14: 3528 ÷ 14 : Remainder = 0
  • Divide 3528 by 18: 3528 ÷ 18 : Remainder = 0
  • Divide 3528 by 21: 3528 ÷ 21 : Remainder = 0
  • Divide 3528 by 24: 3528 ÷ 24 : Remainder = 0
  • Divide 3528 by 28: 3528 ÷ 28 : Remainder = 0
  • Divide 3528 by 36: 3528 ÷ 36 : Remainder = 0
  • Divide 3528 by 42: 3528 ÷ 42 : Remainder = 0
  • Divide 3528 by 49: 3528 ÷ 49 : Remainder = 0
  • Divide 3528 by 56: 3528 ÷ 56 : Remainder = 0
  • Divide 3528 by 63: 3528 ÷ 63 : Remainder = 0
  • Divide 3528 by 72: 3528 ÷ 72 : Remainder = 0
  • Divide 3528 by 84: 3528 ÷ 84 : Remainder = 0
  • Divide 3528 by 98: 3528 ÷ 98 : Remainder = 0
  • Divide 3528 by 126: 3528 ÷ 126 : Remainder = 0
  • Divide 3528 by 147: 3528 ÷ 147 : Remainder = 0
  • Divide 3528 by 168: 3528 ÷ 168 : Remainder = 0
  • Divide 3528 by 196: 3528 ÷ 196 : Remainder = 0
  • Divide 3528 by 252: 3528 ÷ 252 : Remainder = 0
  • Divide 3528 by 294: 3528 ÷ 294 : Remainder = 0
  • Divide 3528 by 392: 3528 ÷ 392 : Remainder = 0
  • Divide 3528 by 441: 3528 ÷ 441 : Remainder = 0
  • Divide 3528 by 504: 3528 ÷ 504 : Remainder = 0
  • Divide 3528 by 588: 3528 ÷ 588 : Remainder = 0
  • Divide 3528 by 882: 3528 ÷ 882 : Remainder = 0
  • Divide 3528 by 1176: 3528 ÷ 1176 : Remainder = 0
  • Divide 3528 by 1764: 3528 ÷ 1764 : Remainder = 0
  • Divide 3528 by 3528: 3528 ÷ 3528 : Remainder = 0

Hence, Factors of 3528 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 49, 56, 63, 72, 84, 98, 126, 147, 168, 196, 252, 294, 392, 441, 504, 588, 882, 1176, 1764, and 3528

2. Steps to find factors of 3528 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 3528 using the division method, follow these steps:

  • Step 1. Start dividing 3528 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 3528, which is 2. Divide 3528 by 2 to obtain the quotient (1764).
    3528 ÷ 2 = 1764
  • Step 3. Repeat step 1 with the obtained quotient (1764).
    1764 ÷ 2 = 882
    882 ÷ 2 = 441
    441 ÷ 3 = 147
    147 ÷ 3 = 49
    49 ÷ 7 = 7
    7 ÷ 7 = 1

So, the prime factorization of 3528 is, 3528 = 2 x 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 3528 as shown below:

So, the prime factorization of 3528 is, 3528 = 2 x 2 x 2 x 3 x 3 x 7 x 7.

3. Find factors of 3528 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 3528 would be the two numbers which, when multiplied, give 3528 as the result.

The following table represents the calculation of factors of 3528 in pairs:

Factor Pair Pair Factorization
1 and 3528 1 x 3528 = 3528
2 and 1764 2 x 1764 = 3528
3 and 1176 3 x 1176 = 3528
4 and 882 4 x 882 = 3528
6 and 588 6 x 588 = 3528
7 and 504 7 x 504 = 3528
8 and 441 8 x 441 = 3528
9 and 392 9 x 392 = 3528
12 and 294 12 x 294 = 3528
14 and 252 14 x 252 = 3528
18 and 196 18 x 196 = 3528
21 and 168 21 x 168 = 3528
24 and 147 24 x 147 = 3528
28 and 126 28 x 126 = 3528
36 and 98 36 x 98 = 3528
42 and 84 42 x 84 = 3528
49 and 72 49 x 72 = 3528
56 and 63 56 x 63 = 3528

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 3528. They are called negative pair factors.

Hence, the negative pairs of 3528 would be ( -1 , -3528 ) , ( -2 , -1764 ) , ( -3 , -1176 ) , ( -4 , -882 ) , ( -6 , -588 ) , ( -7 , -504 ) , ( -8 , -441 ) , ( -9 , -392 ) , ( -12 , -294 ) , ( -14 , -252 ) , ( -18 , -196 ) , ( -21 , -168 ) , ( -24 , -147 ) , ( -28 , -126 ) , ( -36 , -98 ) , ( -42 , -84 ) , ( -49 , -72 ) and ( -56 , -63 ) .

What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

Properties of factors

  • Each number is a factor of itself. Eg. 3528 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 3528.
  • Every number is a factor of zero (0), since 3528 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, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 49, 56, 63, 72, 84, 98, 126, 147, 168, 196, 252, 294, 392, 441, 504, 588, 882, 1176, 1764, 3528 are exact divisors of 3528.
  • Factors of 3528 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 49, 56, 63, 72, 84, 98, 126, 147, 168, 196, 252, 294, 392, 441, 504, 588, 882, 1176, 1764, 3528. Each factor divides 3528 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 49, 56, 63, 72, 84, 98, 126, 147, 168, 196, 252, 294, 392, 441, 504, 588, 882, 1176, 1764, 3528 are all less than or equal to 3528.

Frequently Asked Questions

  • Which is the smallest prime factor of 3528?

    Smallest prime factor of 3528 is 2.

  • Is 3528 a perfect square?

    No 3528 is not a perfect square.

  • What are five multiples of 3528?

    First five multiples of 3528 are 7056, 10584, 14112, 17640, 21168.

  • What is prime factorization of 3528?

    Prime factorization of 3528 is 2 x 2 x 2 x 3 x 3 x 7 x 7.

  • What are factors of 3528?

    Factors of 3528 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 49, 56, 63, 72, 84, 98, 126, 147, 168, 196, 252, 294, 392, 441, 504, 588, 882, 1176, 1764, 3528.

  • How do you find factors of a negative number? ( eg. -3528 )?

    Factors of -3528 are -1, -2, -3, -4, -6, -7, -8, -9, -12, -14, -18, -21, -24, -28, -36, -42, -49, -56, -63, -72, -84, -98, -126, -147, -168, -196, -252, -294, -392, -441, -504, -588, -882, -1176, -1764, -3528.

  • Is 3528 a whole number?

    Yes 3528 is a whole number.

  • Which is greatest factor of 3528?

    The greatest factor of 3528 is 1764.

  • What are the prime factors of 3528?

    The factors of 3528 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 49, 56, 63, 72, 84, 98, 126, 147, 168, 196, 252, 294, 392, 441, 504, 588, 882, 1176, 1764, 3528.
    Prime factors of 3528 are 2, 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 3528. Can you help her?

Prime factors of 3528 are 2, 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 3528?

Factors of 3528 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 49, 56, 63, 72, 84, 98, 126, 147, 168, 196, 252, 294, 392, 441, 504, 588, 882, 1176, 1764, 3528.
Even factors of 3528 are 2, 4, 6, 8, 12, 14, 18, 24, 28, 36, 42, 56, 72, 84, 98, 126, 168, 196, 252, 294, 392, 504, 588, 882, 1176, 1764, 3528.
Hence, product of even factors of 3528 is; 2 x 4 x 6 x 8 x 12 x 14 x 18 x 24 x 28 x 36 x 42 x 56 x 72 x 84 x 98 x 126 x 168 x 196 x 252 x 294 x 392 x 504 x 588 x 882 x 1176 x 1764 x 3528 = 9.026943488964407e+51.

Joy wants to calculate mean of all the factors of 3528. Help him in finding the mean of 3528.

Factors of 3528 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 49, 56, 63, 72, 84, 98, 126, 147, 168, 196, 252, 294, 392, 441, 504, 588, 882, 1176, 1764, 3528.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 3528 is 1 + 2 + 3 + 4 + 6 + 7 + 8 + 9 + 12 + 14 + 18 + 21 + 24 + 28 + 36 + 42 + 49 + 56 + 63 + 72 + 84 + 98 + 126 + 147 + 168 + 196 + 252 + 294 + 392 + 441 + 504 + 588 + 882 + 1176 + 1764 + 3528 = 11115.
Hence, the mean of factors of 3528 is 11115 ÷ 36 = 308.75.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 3528? Help her in writing all the factors.

Positive factors are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 49, 56, 63, 72, 84, 98, 126, 147, 168, 196, 252, 294, 392, 441, 504, 588, 882, 1176, 1764, 3528.
Negative factors are -1, -2, -3, -4, -6, -7, -8, -9, -12, -14, -18, -21, -24, -28, -36, -42, -49, -56, -63, -72, -84, -98, -126, -147, -168, -196, -252, -294, -392, -441, -504, -588, -882, -1176, -1764, -3528.

How many factors are there for 3528?

Factors of 3528 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 49, 56, 63, 72, 84, 98, 126, 147, 168, 196, 252, 294, 392, 441, 504, 588, 882, 1176, 1764, 3528.
So there are in total 36 factors.

Joey wants to write all the prime factors of 3528 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 3528 are 2, 2, 2, 3, 3, 7, 7.
So in exponential form it can be written as 23 x 32 x 72.

Kevin has been asked to write 35 factor(s) of 3528. Can you predict the answer?

35 factor(s) of 3528 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 49, 56, 63, 72, 84, 98, 126, 147, 168, 196, 252, 294, 392, 441, 504, 588, 882, 1176, 1764.