Factors of 3780 are 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 27, 28, 30, 35, 36, 42, 45, 54, 60, 63, 70, 84, 90, 105, 108, 126, 135, 140, 180, 189, 210, 252, 270, 315, 378, 420, 540, 630, 756, 945, 1260, 1890, and 3780

How to find factors of a number

1. Steps to find factors of 3780 using Division Method

Example: Find factors of 3780

  • Divide 3780 by 1: 3780 ÷ 1 : Remainder = 0
  • Divide 3780 by 2: 3780 ÷ 2 : Remainder = 0
  • Divide 3780 by 3: 3780 ÷ 3 : Remainder = 0
  • Divide 3780 by 4: 3780 ÷ 4 : Remainder = 0
  • Divide 3780 by 5: 3780 ÷ 5 : Remainder = 0
  • Divide 3780 by 6: 3780 ÷ 6 : Remainder = 0
  • Divide 3780 by 7: 3780 ÷ 7 : Remainder = 0
  • Divide 3780 by 9: 3780 ÷ 9 : Remainder = 0
  • Divide 3780 by 10: 3780 ÷ 10 : Remainder = 0
  • Divide 3780 by 12: 3780 ÷ 12 : Remainder = 0
  • Divide 3780 by 14: 3780 ÷ 14 : Remainder = 0
  • Divide 3780 by 15: 3780 ÷ 15 : Remainder = 0
  • Divide 3780 by 18: 3780 ÷ 18 : Remainder = 0
  • Divide 3780 by 20: 3780 ÷ 20 : Remainder = 0
  • Divide 3780 by 21: 3780 ÷ 21 : Remainder = 0
  • Divide 3780 by 27: 3780 ÷ 27 : Remainder = 0
  • Divide 3780 by 28: 3780 ÷ 28 : Remainder = 0
  • Divide 3780 by 30: 3780 ÷ 30 : Remainder = 0
  • Divide 3780 by 35: 3780 ÷ 35 : Remainder = 0
  • Divide 3780 by 36: 3780 ÷ 36 : Remainder = 0
  • Divide 3780 by 42: 3780 ÷ 42 : Remainder = 0
  • Divide 3780 by 45: 3780 ÷ 45 : Remainder = 0
  • Divide 3780 by 54: 3780 ÷ 54 : Remainder = 0
  • Divide 3780 by 60: 3780 ÷ 60 : Remainder = 0
  • Divide 3780 by 63: 3780 ÷ 63 : Remainder = 0
  • Divide 3780 by 70: 3780 ÷ 70 : Remainder = 0
  • Divide 3780 by 84: 3780 ÷ 84 : Remainder = 0
  • Divide 3780 by 90: 3780 ÷ 90 : Remainder = 0
  • Divide 3780 by 105: 3780 ÷ 105 : Remainder = 0
  • Divide 3780 by 108: 3780 ÷ 108 : Remainder = 0
  • Divide 3780 by 126: 3780 ÷ 126 : Remainder = 0
  • Divide 3780 by 135: 3780 ÷ 135 : Remainder = 0
  • Divide 3780 by 140: 3780 ÷ 140 : Remainder = 0
  • Divide 3780 by 180: 3780 ÷ 180 : Remainder = 0
  • Divide 3780 by 189: 3780 ÷ 189 : Remainder = 0
  • Divide 3780 by 210: 3780 ÷ 210 : Remainder = 0
  • Divide 3780 by 252: 3780 ÷ 252 : Remainder = 0
  • Divide 3780 by 270: 3780 ÷ 270 : Remainder = 0
  • Divide 3780 by 315: 3780 ÷ 315 : Remainder = 0
  • Divide 3780 by 378: 3780 ÷ 378 : Remainder = 0
  • Divide 3780 by 420: 3780 ÷ 420 : Remainder = 0
  • Divide 3780 by 540: 3780 ÷ 540 : Remainder = 0
  • Divide 3780 by 630: 3780 ÷ 630 : Remainder = 0
  • Divide 3780 by 756: 3780 ÷ 756 : Remainder = 0
  • Divide 3780 by 945: 3780 ÷ 945 : Remainder = 0
  • Divide 3780 by 1260: 3780 ÷ 1260 : Remainder = 0
  • Divide 3780 by 1890: 3780 ÷ 1890 : Remainder = 0
  • Divide 3780 by 3780: 3780 ÷ 3780 : Remainder = 0

Hence, Factors of 3780 are 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 27, 28, 30, 35, 36, 42, 45, 54, 60, 63, 70, 84, 90, 105, 108, 126, 135, 140, 180, 189, 210, 252, 270, 315, 378, 420, 540, 630, 756, 945, 1260, 1890, and 3780

2. Steps to find factors of 3780 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 3780 using the division method, follow these steps:

  • Step 1. Start dividing 3780 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 3780, which is 2. Divide 3780 by 2 to obtain the quotient (1890).
    3780 ÷ 2 = 1890
  • Step 3. Repeat step 1 with the obtained quotient (1890).
    1890 ÷ 2 = 945
    945 ÷ 3 = 315
    315 ÷ 3 = 105
    105 ÷ 3 = 35
    35 ÷ 5 = 7
    7 ÷ 7 = 1

So, the prime factorization of 3780 is, 3780 = 2 x 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 3780 as shown below:

So, the prime factorization of 3780 is, 3780 = 2 x 2 x 3 x 3 x 3 x 5 x 7.

3. Find factors of 3780 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 3780 would be the two numbers which, when multiplied, give 3780 as the result.

The following table represents the calculation of factors of 3780 in pairs:

Factor Pair Pair Factorization
1 and 3780 1 x 3780 = 3780
2 and 1890 2 x 1890 = 3780
3 and 1260 3 x 1260 = 3780
4 and 945 4 x 945 = 3780
5 and 756 5 x 756 = 3780
6 and 630 6 x 630 = 3780
7 and 540 7 x 540 = 3780
9 and 420 9 x 420 = 3780
10 and 378 10 x 378 = 3780
12 and 315 12 x 315 = 3780
14 and 270 14 x 270 = 3780
15 and 252 15 x 252 = 3780
18 and 210 18 x 210 = 3780
20 and 189 20 x 189 = 3780
21 and 180 21 x 180 = 3780
27 and 140 27 x 140 = 3780
28 and 135 28 x 135 = 3780
30 and 126 30 x 126 = 3780
35 and 108 35 x 108 = 3780
36 and 105 36 x 105 = 3780
42 and 90 42 x 90 = 3780
45 and 84 45 x 84 = 3780
54 and 70 54 x 70 = 3780
60 and 63 60 x 63 = 3780

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 3780. They are called negative pair factors.

Hence, the negative pairs of 3780 would be ( -1 , -3780 ) , ( -2 , -1890 ) , ( -3 , -1260 ) , ( -4 , -945 ) , ( -5 , -756 ) , ( -6 , -630 ) , ( -7 , -540 ) , ( -9 , -420 ) , ( -10 , -378 ) , ( -12 , -315 ) , ( -14 , -270 ) , ( -15 , -252 ) , ( -18 , -210 ) , ( -20 , -189 ) , ( -21 , -180 ) , ( -27 , -140 ) , ( -28 , -135 ) , ( -30 , -126 ) , ( -35 , -108 ) , ( -36 , -105 ) , ( -42 , -90 ) , ( -45 , -84 ) , ( -54 , -70 ) and ( -60 , -63 ) .

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. 3780 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 3780.
  • Every number is a factor of zero (0), since 3780 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, 9, 10, 12, 14, 15, 18, 20, 21, 27, 28, 30, 35, 36, 42, 45, 54, 60, 63, 70, 84, 90, 105, 108, 126, 135, 140, 180, 189, 210, 252, 270, 315, 378, 420, 540, 630, 756, 945, 1260, 1890, 3780 are exact divisors of 3780.
  • Factors of 3780 are 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 27, 28, 30, 35, 36, 42, 45, 54, 60, 63, 70, 84, 90, 105, 108, 126, 135, 140, 180, 189, 210, 252, 270, 315, 378, 420, 540, 630, 756, 945, 1260, 1890, 3780. Each factor divides 3780 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, 9, 10, 12, 14, 15, 18, 20, 21, 27, 28, 30, 35, 36, 42, 45, 54, 60, 63, 70, 84, 90, 105, 108, 126, 135, 140, 180, 189, 210, 252, 270, 315, 378, 420, 540, 630, 756, 945, 1260, 1890, 3780 are all less than or equal to 3780.

Frequently Asked Questions

  • Which is the smallest prime factor of 3780?

    Smallest prime factor of 3780 is 2.

  • Is 3780 a perfect square?

    No 3780 is not a perfect square.

  • What are five multiples of 3780?

    First five multiples of 3780 are 7560, 11340, 15120, 18900, 22680.

  • What is prime factorization of 3780?

    Prime factorization of 3780 is 2 x 2 x 3 x 3 x 3 x 5 x 7.

  • What are factors of 3780?

    Factors of 3780 are 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 27, 28, 30, 35, 36, 42, 45, 54, 60, 63, 70, 84, 90, 105, 108, 126, 135, 140, 180, 189, 210, 252, 270, 315, 378, 420, 540, 630, 756, 945, 1260, 1890, 3780.

  • How do you find factors of a negative number? ( eg. -3780 )?

    Factors of -3780 are -1, -2, -3, -4, -5, -6, -7, -9, -10, -12, -14, -15, -18, -20, -21, -27, -28, -30, -35, -36, -42, -45, -54, -60, -63, -70, -84, -90, -105, -108, -126, -135, -140, -180, -189, -210, -252, -270, -315, -378, -420, -540, -630, -756, -945, -1260, -1890, -3780.

  • Is 3780 a whole number?

    Yes 3780 is a whole number.

  • Which is greatest factor of 3780?

    The greatest factor of 3780 is 1890.

  • What are the prime factors of 3780?

    The factors of 3780 are 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 27, 28, 30, 35, 36, 42, 45, 54, 60, 63, 70, 84, 90, 105, 108, 126, 135, 140, 180, 189, 210, 252, 270, 315, 378, 420, 540, 630, 756, 945, 1260, 1890, 3780.
    Prime factors of 3780 are 2, 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 3780. Can you help her?

Prime factors of 3780 are 2, 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 3780?

Factors of 3780 are 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 27, 28, 30, 35, 36, 42, 45, 54, 60, 63, 70, 84, 90, 105, 108, 126, 135, 140, 180, 189, 210, 252, 270, 315, 378, 420, 540, 630, 756, 945, 1260, 1890, 3780.
Even factors of 3780 are 2, 4, 6, 10, 12, 14, 18, 20, 28, 30, 36, 42, 54, 60, 70, 84, 90, 108, 126, 140, 180, 210, 252, 270, 378, 420, 540, 630, 756, 1260, 1890, 3780.
Hence, product of even factors of 3780 is; 2 x 4 x 6 x 10 x 12 x 14 x 18 x 20 x 28 x 30 x 36 x 42 x 54 x 60 x 70 x 84 x 90 x 108 x 126 x 140 x 180 x 210 x 252 x 270 x 378 x 420 x 540 x 630 x 756 x 1260 x 1890 x 3780 = 1.1385411400135844e+62.

Joy wants to calculate mean of all the factors of 3780. Help him in finding the mean of 3780.

Factors of 3780 are 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 27, 28, 30, 35, 36, 42, 45, 54, 60, 63, 70, 84, 90, 105, 108, 126, 135, 140, 180, 189, 210, 252, 270, 315, 378, 420, 540, 630, 756, 945, 1260, 1890, 3780.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 3780 is 1 + 2 + 3 + 4 + 5 + 6 + 7 + 9 + 10 + 12 + 14 + 15 + 18 + 20 + 21 + 27 + 28 + 30 + 35 + 36 + 42 + 45 + 54 + 60 + 63 + 70 + 84 + 90 + 105 + 108 + 126 + 135 + 140 + 180 + 189 + 210 + 252 + 270 + 315 + 378 + 420 + 540 + 630 + 756 + 945 + 1260 + 1890 + 3780 = 13440.
Hence, the mean of factors of 3780 is 13440 ÷ 48 = 280.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 3780? Help her in writing all the factors.

Positive factors are 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 27, 28, 30, 35, 36, 42, 45, 54, 60, 63, 70, 84, 90, 105, 108, 126, 135, 140, 180, 189, 210, 252, 270, 315, 378, 420, 540, 630, 756, 945, 1260, 1890, 3780.
Negative factors are -1, -2, -3, -4, -5, -6, -7, -9, -10, -12, -14, -15, -18, -20, -21, -27, -28, -30, -35, -36, -42, -45, -54, -60, -63, -70, -84, -90, -105, -108, -126, -135, -140, -180, -189, -210, -252, -270, -315, -378, -420, -540, -630, -756, -945, -1260, -1890, -3780.

How many factors are there for 3780?

Factors of 3780 are 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 27, 28, 30, 35, 36, 42, 45, 54, 60, 63, 70, 84, 90, 105, 108, 126, 135, 140, 180, 189, 210, 252, 270, 315, 378, 420, 540, 630, 756, 945, 1260, 1890, 3780.
So there are in total 48 factors.

Joey wants to write all the prime factors of 3780 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 3780 are 2, 2, 3, 3, 3, 5, 7.
So in exponential form it can be written as 22 x 33 x 5 x 7.

Kevin has been asked to write 47 factor(s) of 3780. Can you predict the answer?

47 factor(s) of 3780 are 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 27, 28, 30, 35, 36, 42, 45, 54, 60, 63, 70, 84, 90, 105, 108, 126, 135, 140, 180, 189, 210, 252, 270, 315, 378, 420, 540, 630, 756, 945, 1260, 1890.