6493 LearnersLast updated on May 26th, 2025
Factors of 1620
Factors of 1620 are numbers that can divide 1620 completely without any remainder. Understanding factors is useful for organizing events and seating arrangements in everyday life. In this topic, we will explore the factors of 1620 and different methods to find them.
What are the Factors of 1620?
The factors of 1620 are numbers that divide 1620 without leaving a remainder.
Positive Factors: These are the positive numbers that divide 1620 evenly. Positive factors: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 45, 54, 60, 65, 72, 81, 90, 108, 135, 162, 180, 270, 324, 405, 540, 810, 1620
Negative Factors: These are the negative counterparts of the positive factors. Negative factors: -1, -2, -3, -4, -5, -6, -8, -9, -10, -12, -15, -18, -20, -24, -27, -30, -36, -45, -54, -60, -65, -72, -81, -90, -108, -135, -162, -180, -270, -324, -405, -540, -810, -1620
Prime Factors: Prime factors are the prime numbers that, when multiplied together, give 1620 as the product. Prime factors of 1620: 2, 3, 5
Prime Factorization: This involves breaking 1620 down into its prime factors and expressing it as a product. Prime factorization of 1620: 22 × 34 × 51
How to Find the Factors of 1620?
There are different methods to find the factors of 1620.
Methods to Find the Factors of 1620:
- Multiplication Method
- Division Method
- Prime Factor and Prime Factorization
- Factor Tree
These approaches help in understanding the different factors of 1620, both positive and negative, and how prime factorization works for this number.
Finding Factors Using the Multiplication Method
The multiplication method identifies pairs of factors whose product is 1620.
Step 1: Identify pairs of numbers whose product equals 1620.
Step 2: List these numbers as factors.
Example pairs for 1620 include: 1 × 1620 = 1620, 2 × 810 = 1620, 3 × 540 = 1620, 4 × 405 = 1620, and so on.
Finding Factors Using the Division Method
The division method identifies numbers that divide 1620 evenly.
Step 1: Start with 1, as all numbers are divisible by 1.
Step 2: Proceed to other integers and check divisibility.
Step 3: List numbers that divide 1620 completely.
Prime Factors and Prime Factorization
Prime Factors of 1620: The prime numbers that multiply to give 1620 are 2, 3, and 5.
Prime Factorization: To find the prime factorization, divide 1620 by its prime factors:
- 1620 ÷ 2 = 810
- 810 ÷ 2 = 405
- 405 ÷ 3 = 135
- 135 ÷ 3 = 45
- 45 ÷ 3 = 15
- 15 ÷ 3 = 5
- 5 ÷ 5 = 1
Prime factorization of 1620: 22 × 34 × 51
Factor Tree
A factor tree visually shows how 1620 breaks down into its prime factors:
This tree shows the breakdown of 1620 into its prime factors: 2 × 3 × 5.
In this factor tree, each branch splits into prime factors.
Common Mistakes and How to Avoid Them in Factors of 1620
Overlooking larger prime factors.
Mistake 1
Overlooking larger prime factors.
Ensure to include all prime factors, even larger ones like 5, in the factorization.
Factors of 1620 Examples
Problem 1
Can you check whether 90 and 1620 are co-prime?
No, 90 and 1620 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 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Factors of 1620: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 81, 90, 108, 135, 162, 180, 270, 324, 405, 540, 810, 1620
Here, the GCF is 90. So, 90 and 1620 are not co-prime. For co-prime, the GCF of numbers should be 1.
Problem 2
Verify whether 1620 is a multiple of 45
Yes, 1620 is a multiple of 45
Explanation
Multiples of 45 are numbers we get when 45 is multiplied by another number. 1620 ÷ 45 = 36, which is a whole number. Therefore, 1620 is a multiple of 45.
Problem 3
Identify the perfect square from the factors of 1620
The perfect square factor of 1620 is 81 and the root is 9
Explanation
A perfect square is a number we get when the same number is multiplied twice. When 9 is multiplied twice (9×9), we get the perfect square 81.
Problem 4
What are the factors of 1620?
The factors of 1620 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 81, 90, 108, 135, 162, 180, 270, 324, 405, 540, 810, 1620
Explanation
Factors are the numbers that divide the given number without leaving a remainder. Listing all the divisors of 1620 provides the complete list of factors.
Problem 5
How do you determine if a number is a factor of 1620?
To determine if a number is a factor of 1620, divide 1620 by that number and check if the result is a whole number.
Explanation
If 1620 divided by a number gives a whole number without a remainder, then that number is a factor of 1620. For example, 1620 ÷ 45 = 36, which is a whole number, so 45 is a factor of 1620.
FAQs on Factors of 1620
1.What are the factors of 1620?
2.How do you determine if a number is a factor of 1620?
3.What is the smallest factor of 1620?
4.What is the largest factor of 1620?
5.How many factors does 1620 have?
6.How many odd factors does 1620 have?
7.What factors go into 1620?
8.Do any perfect squares exist in the factors of 1620?
Important glossaries for the Factors of 1620
- Co-prime: Numbers that do not share any common factors other than 1.
- Perfect Square: A number obtained when a whole number is multiplied by itself (e.g., 9 × 9 = 81).
- Prime Factors: Prime numbers that, when multiplied together, produce the original number (e.g., for 1620, the prime factors are 2, 3, and 5).
- Factor Tree: A diagram that breaks down a number into its prime factors, showing how the number can be divided step by step.
- Multiple: A number obtained when another number is multiplied by an integer (e.g., 45, 90, 135 are multiples of 45).
Explore More numbers
Previous to Factors of 1620
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.
