Last updated on May 26th, 2025
Factors of 1155 are numbers that can divide 1155 completely without a remainder. We often use factors in organizing events, solving problems, and various real-life applications. In this topic, we will explore the factors of 1155 and the different methods to find them.
The factors of 1155 are 1, 3, 5, 7, 11, 15, 21, 33, 35, 55, 77, 105, 165, 231, 385, and 1155.
Positive Factors: These are positive integers that divide 1155 completely.
Positive factors: 1, 3, 5, 7, 11, 15, 21, 33, 35, 55, 77, 105, 165, 231, 385, 1155.
Negative Factors: These are negative counterparts of the positive factors.
Negative factors: -1, -3, -5, -7, -11, -15, -21, -33, -35, -55, -77, -105, -165, -231, -385, -1155.
Prime Factors: Prime factors are the prime numbers that multiply together to give 1155 as the product.
Prime factors: 3, 5, 7, 11.
Prime Factorization: Prime factorization involves breaking 1155 into its prime factors.
It is expressed as 3×5×7×113 \times 5 \times 7 \times 113×5×7×11.
This breakdown helps in understanding the various factors of 1155, whether they are positive or negative, as well as how prime factorization works for this number.
There are various methods to find the factors of 1155:
Methods to Find the Factors of 1155:
The multiplication method finds the pair of factors that give 1155 as their product.
Step 1: Find the pair of numbers whose product is 1155.
Step 2: The factors are those numbers that, when multiplied, give 1155.
Step 3: Make a list of numbers whose product will be 1155.
A list of numbers whose products are 1155 is given below:
Thus, the factors of 1155 are 1, 3, 5, 7, 11, 15, 21, 33, 35, 55, 77, 105, 165, 231, 385, and 1155.
The division method finds the numbers that fully divide the given number.
Step 1: Start by dividing 1155 by 1, as every number is divisible by 1.
Example: 1155÷1=11551155 \div 1 = 11551155÷1=1155.
Step 2: Move to the next integers and check for divisibility. Factors of 1155 are all numbers that divide it completely.
Thus, the factors of 1155 are 1, 3, 5, 7, 11, 15, 21, 33, 35, 55, 77, 105, 165, 231, 385, and 1155.
Prime factorization breaks down 1155 into its prime factors.
Step 1: Divide 1155 by the smallest prime number (3):
1155÷3=385.
Step 2: Divide 385 by the next smallest prime number (5):
385÷5=77.
Step 3: Divide 77 by the next prime number (7):
77÷7=11.
Step 4: Finally, 11 is a prime number.
Prime Factorization of 1155:
Expressed as 3×5×7×11
The prime factorization is visually represented using the factor tree. It helps to understand the process easily.
This tree shows the breakdown of 1155 into its prime factors: 3×5×7×113 \times 5 \times 7 \times 113×5×7×11.
In this factor tree, each branch splits into prime factors.
Factors of 1155 in Pairs
Factors of 1155 can be written in both positive pairs and negative pairs. Their product will equal 1155.
Positive Factor Pairs:
(1, 1155), (3, 385), (5, 231), (7, 165), (11, 105), (15, 77), (21, 55), (33, 35).
Negative Factor Pairs:
(-1, -1155), (-3, -385), (-5, -231), (-7, -165), (-11, -105), (-15, -77), (-21, -55), (-33, -35).
Mistakes can happen when finding the factors of 1155. Below are some common errors and tips on how to avoid them for accurate factor identification.
Can you check whether 1155 and 35 are co-prime?
No, 1155 and 35 are not co-prime.
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 1155: 1, 3, 5, 7, 11, 15, 21, 33, 35, 77, 105, 165, 231, 385, 1155
Factors of 35: 1, 5, 7, 35
Here, the GCF is 35. So 1155 and 35 are not co-prime.
For co-prime, the GCF of numbers should be 1.
Verify whether 1155 is a multiple of 9.
No, 1155 is not a multiple of 9.
Multiples of 9 are numbers we get when 9 is multiplied by another number.
No number can be multiplied by 9 to get 1155 as the product.
Identify the perfect square from the factors of 1155.
The perfect square factor of 1155 is 121, and the root is 11.
A perfect square is a number we get when the same number is multiplied twice.
When 11 is multiplied twice (11×11), we get the perfect square 121.
Is 1155 divisible by 6?
No, 1155 is not divisible by 6.
For a number to be divisible by 6, it must be divisible by both 2 and 3.
1155 is divisible by 3 but not by 2 (since it is not even).
How many factors does 1155 have?
1155 has 15 factors.
The factors of 1155 are 1, 3, 5, 7, 11, 15, 21, 33, 35, 77, 105, 165, 231, 385, 1155.
Counting these, we find there are 15 factors.
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.
: She loves to read number jokes and games.