Factors of 4200 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 25, 28, 30, 35, 40, 42, 50, 56, 60, 70, 75, 84, 100, 105, 120, 140, 150, 168, 175, 200, 210, 280, 300, 350, 420, 525, 600, 700, 840, 1050, 1400, 2100, and 4200

How to find factors of a number

1. Steps to find factors of 4200 using Division Method

Example: Find factors of 4200

  • Divide 4200 by 1: 4200 ÷ 1 : Remainder = 0
  • Divide 4200 by 2: 4200 ÷ 2 : Remainder = 0
  • Divide 4200 by 3: 4200 ÷ 3 : Remainder = 0
  • Divide 4200 by 4: 4200 ÷ 4 : Remainder = 0
  • Divide 4200 by 5: 4200 ÷ 5 : Remainder = 0
  • Divide 4200 by 6: 4200 ÷ 6 : Remainder = 0
  • Divide 4200 by 7: 4200 ÷ 7 : Remainder = 0
  • Divide 4200 by 8: 4200 ÷ 8 : Remainder = 0
  • Divide 4200 by 10: 4200 ÷ 10 : Remainder = 0
  • Divide 4200 by 12: 4200 ÷ 12 : Remainder = 0
  • Divide 4200 by 14: 4200 ÷ 14 : Remainder = 0
  • Divide 4200 by 15: 4200 ÷ 15 : Remainder = 0
  • Divide 4200 by 20: 4200 ÷ 20 : Remainder = 0
  • Divide 4200 by 21: 4200 ÷ 21 : Remainder = 0
  • Divide 4200 by 24: 4200 ÷ 24 : Remainder = 0
  • Divide 4200 by 25: 4200 ÷ 25 : Remainder = 0
  • Divide 4200 by 28: 4200 ÷ 28 : Remainder = 0
  • Divide 4200 by 30: 4200 ÷ 30 : Remainder = 0
  • Divide 4200 by 35: 4200 ÷ 35 : Remainder = 0
  • Divide 4200 by 40: 4200 ÷ 40 : Remainder = 0
  • Divide 4200 by 42: 4200 ÷ 42 : Remainder = 0
  • Divide 4200 by 50: 4200 ÷ 50 : Remainder = 0
  • Divide 4200 by 56: 4200 ÷ 56 : Remainder = 0
  • Divide 4200 by 60: 4200 ÷ 60 : Remainder = 0
  • Divide 4200 by 70: 4200 ÷ 70 : Remainder = 0
  • Divide 4200 by 75: 4200 ÷ 75 : Remainder = 0
  • Divide 4200 by 84: 4200 ÷ 84 : Remainder = 0
  • Divide 4200 by 100: 4200 ÷ 100 : Remainder = 0
  • Divide 4200 by 105: 4200 ÷ 105 : Remainder = 0
  • Divide 4200 by 120: 4200 ÷ 120 : Remainder = 0
  • Divide 4200 by 140: 4200 ÷ 140 : Remainder = 0
  • Divide 4200 by 150: 4200 ÷ 150 : Remainder = 0
  • Divide 4200 by 168: 4200 ÷ 168 : Remainder = 0
  • Divide 4200 by 175: 4200 ÷ 175 : Remainder = 0
  • Divide 4200 by 200: 4200 ÷ 200 : Remainder = 0
  • Divide 4200 by 210: 4200 ÷ 210 : Remainder = 0
  • Divide 4200 by 280: 4200 ÷ 280 : Remainder = 0
  • Divide 4200 by 300: 4200 ÷ 300 : Remainder = 0
  • Divide 4200 by 350: 4200 ÷ 350 : Remainder = 0
  • Divide 4200 by 420: 4200 ÷ 420 : Remainder = 0
  • Divide 4200 by 525: 4200 ÷ 525 : Remainder = 0
  • Divide 4200 by 600: 4200 ÷ 600 : Remainder = 0
  • Divide 4200 by 700: 4200 ÷ 700 : Remainder = 0
  • Divide 4200 by 840: 4200 ÷ 840 : Remainder = 0
  • Divide 4200 by 1050: 4200 ÷ 1050 : Remainder = 0
  • Divide 4200 by 1400: 4200 ÷ 1400 : Remainder = 0
  • Divide 4200 by 2100: 4200 ÷ 2100 : Remainder = 0
  • Divide 4200 by 4200: 4200 ÷ 4200 : Remainder = 0

Hence, Factors of 4200 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 25, 28, 30, 35, 40, 42, 50, 56, 60, 70, 75, 84, 100, 105, 120, 140, 150, 168, 175, 200, 210, 280, 300, 350, 420, 525, 600, 700, 840, 1050, 1400, 2100, and 4200

2. Steps to find factors of 4200 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 4200 using the division method, follow these steps:

  • Step 1. Start dividing 4200 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 4200, which is 2. Divide 4200 by 2 to obtain the quotient (2100).
    4200 ÷ 2 = 2100
  • Step 3. Repeat step 1 with the obtained quotient (2100).
    2100 ÷ 2 = 1050
    1050 ÷ 2 = 525
    525 ÷ 3 = 175
    175 ÷ 5 = 35
    35 ÷ 5 = 7
    7 ÷ 7 = 1

So, the prime factorization of 4200 is, 4200 = 2 x 2 x 2 x 3 x 5 x 5 x 7.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 4200 as shown below:

So, the prime factorization of 4200 is, 4200 = 2 x 2 x 2 x 3 x 5 x 5 x 7.

3. Find factors of 4200 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 4200 would be the two numbers which, when multiplied, give 4200 as the result.

The following table represents the calculation of factors of 4200 in pairs:

Factor Pair Pair Factorization
1 and 4200 1 x 4200 = 4200
2 and 2100 2 x 2100 = 4200
3 and 1400 3 x 1400 = 4200
4 and 1050 4 x 1050 = 4200
5 and 840 5 x 840 = 4200
6 and 700 6 x 700 = 4200
7 and 600 7 x 600 = 4200
8 and 525 8 x 525 = 4200
10 and 420 10 x 420 = 4200
12 and 350 12 x 350 = 4200
14 and 300 14 x 300 = 4200
15 and 280 15 x 280 = 4200
20 and 210 20 x 210 = 4200
21 and 200 21 x 200 = 4200
24 and 175 24 x 175 = 4200
25 and 168 25 x 168 = 4200
28 and 150 28 x 150 = 4200
30 and 140 30 x 140 = 4200
35 and 120 35 x 120 = 4200
40 and 105 40 x 105 = 4200
42 and 100 42 x 100 = 4200
50 and 84 50 x 84 = 4200
56 and 75 56 x 75 = 4200
60 and 70 60 x 70 = 4200

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 4200. They are called negative pair factors.

Hence, the negative pairs of 4200 would be ( -1 , -4200 ) , ( -2 , -2100 ) , ( -3 , -1400 ) , ( -4 , -1050 ) , ( -5 , -840 ) , ( -6 , -700 ) , ( -7 , -600 ) , ( -8 , -525 ) , ( -10 , -420 ) , ( -12 , -350 ) , ( -14 , -300 ) , ( -15 , -280 ) , ( -20 , -210 ) , ( -21 , -200 ) , ( -24 , -175 ) , ( -25 , -168 ) , ( -28 , -150 ) , ( -30 , -140 ) , ( -35 , -120 ) , ( -40 , -105 ) , ( -42 , -100 ) , ( -50 , -84 ) , ( -56 , -75 ) and ( -60 , -70 ) .

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. 4200 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 4200.
  • Every number is a factor of zero (0), since 4200 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, 8, 10, 12, 14, 15, 20, 21, 24, 25, 28, 30, 35, 40, 42, 50, 56, 60, 70, 75, 84, 100, 105, 120, 140, 150, 168, 175, 200, 210, 280, 300, 350, 420, 525, 600, 700, 840, 1050, 1400, 2100, 4200 are exact divisors of 4200.
  • Factors of 4200 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 25, 28, 30, 35, 40, 42, 50, 56, 60, 70, 75, 84, 100, 105, 120, 140, 150, 168, 175, 200, 210, 280, 300, 350, 420, 525, 600, 700, 840, 1050, 1400, 2100, 4200. Each factor divides 4200 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, 8, 10, 12, 14, 15, 20, 21, 24, 25, 28, 30, 35, 40, 42, 50, 56, 60, 70, 75, 84, 100, 105, 120, 140, 150, 168, 175, 200, 210, 280, 300, 350, 420, 525, 600, 700, 840, 1050, 1400, 2100, 4200 are all less than or equal to 4200.

Frequently Asked Questions

  • How do you find factors of a negative number? ( eg. -4200 )?

    Factors of -4200 are -1, -2, -3, -4, -5, -6, -7, -8, -10, -12, -14, -15, -20, -21, -24, -25, -28, -30, -35, -40, -42, -50, -56, -60, -70, -75, -84, -100, -105, -120, -140, -150, -168, -175, -200, -210, -280, -300, -350, -420, -525, -600, -700, -840, -1050, -1400, -2100, -4200.

  • What is the sum of all factors of 4200?

    The sum of all factors of 4200 is 14880.

  • What is prime factorization of 4200?

    Prime factorization of 4200 is 2 x 2 x 2 x 3 x 5 x 5 x 7.

  • What are the pair factors of 4200?

    Pair factors of 4200 are (1,4200), (2,2100), (3,1400), (4,1050), (5,840), (6,700), (7,600), (8,525), (10,420), (12,350), (14,300), (15,280), (20,210), (21,200), (24,175), (25,168), (28,150), (30,140), (35,120), (40,105), (42,100), (50,84), (56,75), (60,70).

  • What are six multiples of 4200?

    First five multiples of 4200 are 8400, 12600, 16800, 21000, 25200, 29400.

  • Is 4200 a whole number?

    Yes 4200 is a whole number.

  • Which is the smallest prime factor of 4200?

    Smallest prime factor of 4200 is 2.

  • What are five multiples of 4200?

    First five multiples of 4200 are 8400, 12600, 16800, 21000, 25200.

  • Write all factors of 4200?

    Factors of 4200 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 25, 28, 30, 35, 40, 42, 50, 56, 60, 70, 75, 84, 100, 105, 120, 140, 150, 168, 175, 200, 210, 280, 300, 350, 420, 525, 600, 700, 840, 1050, 1400, 2100, 4200.

Examples of Factors

Joey wants to write all the prime factors of 4200 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 4200 are 2, 2, 2, 3, 5, 5, 7.
So in exponential form it can be written as 23 x 3 x 52 x 7.

How many factors are there for 4200?

Factors of 4200 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 25, 28, 30, 35, 40, 42, 50, 56, 60, 70, 75, 84, 100, 105, 120, 140, 150, 168, 175, 200, 210, 280, 300, 350, 420, 525, 600, 700, 840, 1050, 1400, 2100, 4200.
So there are in total 48 factors.

Kevin has been asked to write 47 factor(s) of 4200. Can you predict the answer?

47 factor(s) of 4200 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 25, 28, 30, 35, 40, 42, 50, 56, 60, 70, 75, 84, 100, 105, 120, 140, 150, 168, 175, 200, 210, 280, 300, 350, 420, 525, 600, 700, 840, 1050, 1400, 2100.

Sammy is puzzled while calculating the prime factors of 4200. Can you help him find them?

Factors of 4200 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 25, 28, 30, 35, 40, 42, 50, 56, 60, 70, 75, 84, 100, 105, 120, 140, 150, 168, 175, 200, 210, 280, 300, 350, 420, 525, 600, 700, 840, 1050, 1400, 2100, 4200.
Prime factors of 4200 are 2, 2, 2, 3, 5, 5, 7

What is prime factorization of 4200?

Prime factorization of 4200 is 2 x 2 x 2 x 3 x 5 x 5 x 7 = 23 x 3 x 52 x 7.

Ariel has been assigned the task to find the product of all the prime factors of 4200. Can you help her?

Prime factors of 4200 are 2, 2, 2, 3, 5, 5, 7.
Hence, the product of prime factors of 210.

Can you help Rubel to find out the product of the even factors of 4200?

Factors of 4200 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 25, 28, 30, 35, 40, 42, 50, 56, 60, 70, 75, 84, 100, 105, 120, 140, 150, 168, 175, 200, 210, 280, 300, 350, 420, 525, 600, 700, 840, 1050, 1400, 2100, 4200.
Even factors of 4200 are 2, 4, 6, 8, 10, 12, 14, 20, 24, 28, 30, 40, 42, 50, 56, 60, 70, 84, 100, 120, 140, 150, 168, 200, 210, 280, 300, 350, 420, 600, 700, 840, 1050, 1400, 2100, 4200.
Hence, product of even factors of 4200 is; 2 x 4 x 6 x 8 x 10 x 12 x 14 x 20 x 24 x 28 x 30 x 40 x 42 x 50 x 56 x 60 x 70 x 84 x 100 x 120 x 140 x 150 x 168 x 200 x 210 x 280 x 300 x 350 x 420 x 600 x 700 x 840 x 1050 x 1400 x 2100 x 4200 = 4.3353797936295353e+70.