271 LearnersLast updated on May 26th, 2025
Factors of 4200
Factors of 4200 are numbers that can divide 4200 completely without the remainder. We often use factors like organizing events and seating arrangements in our daily lives. In this topic, we will know more about the factors of 4200 and the different methods to find them.
What are the 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
|
Positive Factors |
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 |
|
Negative Factors |
-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 |
2, 3, 5, 7 |
|
Prime Factorization |
23 × 31 × 52 × 71 |
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.
How to Find the Factors of 4200?
There are different methods to find the factors of 4200.
Methods to find the factors of 4200:
- Multiplication Method
- Division Method
- Prime Factor and Prime Factorization
- Factor Tree
Finding Factors Using Multiplication Method
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.
Finding Factors Using Division Method
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.
Prime Factors and Prime Factorization
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
Factor Tree
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.
Common Mistakes and How to Avoid Them in Factors of 4200
Mistakes can happen when finding the factors of 42. Below are some common errors and tips on how to avoid them for accurate factor identification
Mistake 1
Assuming 7 is the only factor of 4200
Remember that factors are numbers that can divide 4200 completely. So, other numbers that can divide 4200 completely are 1, 2, 3, 4, 5, and so on.
Solved Examples for Factors of 4200
Problem 1
Can you check whether 70 and 84 are co-prime?
No, 70 and 84 are not co-prime
Explanation
To check whether two numbers are co-prime, list their factors first. Once you have listed the factors, identify the common factors and determine the GCF. If the GCF is greater than 1, then the numbers are not co-prime.
Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70
Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Here, the GCF is 14. So, 70 and 84 are not co-prime. For co-prime, the GCF of numbers should be 1.
Problem 2
Verify whether 4200 is divisible by 12
Yes, 4200 is divisible by 12
Explanation
To check divisibility by 12, verify that the number is divisible by both 3 and 4.
Adding the digits of 4200, the sum will be 6, 6 is divisible by 3. It is also divisible by 4 as it is an even number ending in 0. So, 4200 is divisible by 12.
Problem 3
Identify the perfect square from the factors of 4200
A prime factor of 4200 is 2
Explanation
Prime factors are the prime numbers themselves, when multiplied together, give the original number as the product. The prime factorization of 4200 is 2 × 2 × 2 × 2 × 3 × 5 × 5 × 7. Here, 2 is one of the prime factors.
Problem 4
Find a prime factor of 4200
A prime factor of 4200 is 2
Explanation
Prime factors are the prime numbers themselves, when multiplied together, give the original number as the product. The prime factorization of 4200 is 2 × 2 × 2 × 2 × 3 × 5 × 5 × 7. Here, 2 is one of the prime factors.
Problem 5
Is 4200 a multiple of 15?
Yes, 4200 is a multiple of 15
Explanation
To determine if 4200 is a multiple of 15, check if it is divisible by both 3 and 5. Adding the digits of 4200, the sum will be 6, 6 is divisible by 3. It is also divisible by 5 as it is a number ending in 0. So, 4200 is a multiple of 15.
FAQs for Factors of 4200
1.What are the factors of 4200?
2.How do you determine if a number is a factor of 4200?
3.What is the smallest factor of 4200?
4.What is the largest factor of 4200?
5.How many factors does 4200 have?
6.How many odd factors does 4200 have?
7.What factors go into 4200?
8.Do any perfect squares exist in the factors of 4200?
Glossaries for Factors of 4200
- 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.
Explore More numbers
Previous to Factors of 4200
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
