Factors of 4200

The factors of 4200 are the numbers that divide 4200 evenly.

Positive Factors: These are the positive numbers that divide 4200 evenly.

Positive factors are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 84, 100, 105, 120, 140, 168, 175, 200, 210, 280, 300, 336, 420, 600, 700, 840, 1400, and 4200.

Negative Factors: The negative values of the factors of 4200 are:

Negative factors are  -1, -2, -3, -4, -5, -6, -7, -8, -10, -12, -14, -15, -20, -21, -24, -28, -30, -35, -40, -42, -48, -56, -60, -70, -84, -100, -105, -120, -140, -168, -175, -200, -210, -280, -300, -336, -420, -600, -700, -840, -1400, -4200

Prime Factors: Prime factors are the prime numbers themselves, when multiplied together, give 4200 as the product.

Prime factors: 2, 3, 5, 7

Prime Factorization: Prime factorization involves breaking 4200 into its prime factors.

It is expressed as 2³ × 3¹ × 5² × 7¹

Table listing the factors of 4200
 

This breakdown helps in understanding the various factors of 4200, whether they are positive or negative, as well as how prime factorization works for this number.

There are different methods to find the factors of 4200.

Methods to find the factors of 4200:

1. Multiplication Method
2. Division Method
3. Prime Factor and Prime Factorization
4. Factor Tree

The multiplication method finds the pair of factors that give 4200 as their product.

Step 1: Find the pair of numbers whose product is 4200.

Step 2: The factors are those numbers, when multiplied, give 4200.

Step 3: Make a list of numbers whose product will be 4200.

A list of numbers whose products are 4200 is given below:

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

Thus, the factors of 4200 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 84, 100, 105, 120, 140, 168, 175, 200, 210, 280, 300, 336, 420, 600, 700, 840, 1400, and 4200.

The division method finds the numbers that fully divide the given number. The steps are given below:

Step 1: Since every number is divisible by 1, 1 will always be a factor.

Example: 4200÷1 = 4200

Step 2: Move to the next integer. The factors of the number include the number that is used to divide and the number of times the particular number is divided.

Thus, the factors of 4200 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 84, 100, 105, 120, 140, 168, 175, 200, 210, 280, 300, 336, 420, 600, 700, 840, 1400, and 4200.

Multiplying prime numbers to get the given number as their product is called prime factors. A number when it is simplified using the factors of that number and is expressed in the form of prime factors is the prime factorization of a number.

Prime Factors of 4200: Number 4200 has four prime factors.

Prime factors of 4200: 2, 3, 5, 7

To find the prime factors of 4200, we can divide 4200 with the prime numbers like 2, 3, 5, and 7 from the list of factors of 4200.

Step 1: Divide 4200 with the prime number 2

• 4200÷2 = 2100

Step 2: Divide 2100 with the prime number 2

• 2100÷2 = 1050

Step 3: Divide 1050 with the prime number 2

• 1050÷2 = 525

Step 4: Divide 525 with the prime number 3

• 525÷3 = 175

Step 5: Divide 175 with the prime number 5

• 175÷5 = 35

Step 6: Divide 35 with the prime number 5

• 35÷5 = 7

Step 7: Divide 7 with the prime number 7

• 7÷7 = 1

Prime Factorization of 4200: Prime factorization breaks down the prime factors of 4200

Expressed as 2³ × 3¹ × 5² × 7¹

The prime factorization is visually represented using the factor tree. It helps to understand the process easily. In this factor tree, each branch splits into prime factors.

This tree shows the breakdown of 328 into its prime factors: 2 x 3 x 5 x 7

Positive and Negative Factor Pairs of 4200

Factors of 4200 can be written in both positive pairs and negative pairs. They are like team members. Their product will be equal to the number given.

Positive Factor Pairs: (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), (28, 150), (30, 140), (35, 120), (40, 105), (42, 100), (48, 87.5), (56, 75), (60, 70), and so on.

Negative Factor Pairs: (-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), (-28, -150), (-30, -140), (-35, -120), (-40, -105), (-42, -100), (-48, -87.5), (-56, -75), (-60, -70), and so on.

• Factors: Numbers that can divide a given number completely without leaving a remainder.

• Prime Factorization:The process of breaking down a number into its prime factors and expressing it as a product of prime numbers.

• Prime Factors:The factors of a number that also come under prime numbers and when multiplied give the original number as its product.

• Negative Factors: The negative counterparts of the positive factors. These also divide the given number without a remainder, but are negative.

• Multiple: Another name for product or the result that is obtained when multiplication is performed between two numbers.