Factors of 1155

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:

• Multiplication Method

• Division Method

• Prime Factors and Prime Factorization

• Factor Tree

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:

• 1 × 1155 = 1155
• 3 × 385 = 1155
• 5 × 231 = 1155
• 7 × 165 = 1155
• 11 × 105 = 1155
• 15 × 77 = 1155
• 21 × 55 = 1155
• 33 × 35 = 1155

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).
 

• Factors: Numbers that divide a given number completely without leaving a remainder. For example, factors of 1155 include 1, 3, 5, and 1155 itself.

• Prime Factorization: The process of expressing a number as a product of its prime factors. For 1155, it is 3×5×7×11

• Positive Factors: Positive integers that divide a number completely. For 1155, these include 1, 3, 5, etc.

• Factor Tree: A visual representation that breaks a number into its prime factors, showing the division process step-by-step.

• Perfect Square Factor: A factor that is a perfect square, meaning it results from squaring an integer. For example, the perfect square factor of 1155 is 121 (11×11).