238 LearnersLast updated on May 26th, 2025
Factors of 66
Do you know how number tricks work? Most of the number tricks work because of the unique characteristics of each number, i.e., factors. A factor of a number is any number that can evenly divide the number. For distributing objects, we use factors in our daily life.
What are the factors of 66.
The numbers which can evenly divide 66 are the factors of 66. 1, 2, 3, 6, 11, 22, 33, 66 are the factors of 66.
Negative factors of 66: The negative factors of 66 are the negative counterparts of the positive factors. -1, -2, -3, -6, -11, -22, -33, -66 are the negative factors of 66.
Prime factors of 66: A prime number is a number which has only two factors, i.e., 1 and the number itself.
2, 3, and 11 are the prime factors of 66.
Prime factorization of 66: The process of splitting a number into smaller prime numbers is prime factorization. Here, the product of prime numbers is the number itself.
The prime factorization of 66 is 21 × 31 × 111
How to find the factors of 66
Factors of a number is a number which can evenly divide the number. Some methods which are used to find the factor of a 66 are,
- Multiplication method
- Division method
- Prime factors and prime factorization
- Factor tree
Finding factors using multiplication method:
In the multiplication method a pair of numbers are identified, the product of multiplying the number is 66.
Step 1: Find the numbers whose product is 66.
1 × 66 = 66
2 × 33 = 66
3 × 22 = 66
6 × 11 = 66
Step 2: List them as pairs
The pair of factors are (1, 66), (2, 33), (3, 22), (6, 11).
Finding factors by division method
In the division method, we need to check which number can evenly divide 66.
Let’s check the factors of 66 using division method
66 ÷ 1 = 66
66 ÷ 2 = 33
66 ÷ 3 = 22
66 ÷ 6 = 11
So, the factors are 1, 2, 3, 6, 11, 22, 33, and 66.
Prime factors and prime factorization
Prime numbers are the numbers which have only two factors. The process of breaking down a large number into a smaller prime number is prime factorization.
To find the factors of a number prime factorization, we need to follow these steps
Step 1: The given number needs to be divided with the smallest prime number.
Step 2: Now, we need to divide the remainder in step 1 with the prime number. The process is continued till the remainder is a prime number.
Let's use the prime factorization method to find the factors of 66.
The prime factors of 66 are 2, 3, and 11.
2, 3, 5, 7, 11, 13, 17,… are the prime numbers.
Step 1: Checking the divisibility by 2: 66 is an even number, so, it is divisible by 2.
66 ÷ 2 = 33
Step 2: Now, the remainder is 33.
Checking the divisibility by 3: 33 is divisible by 3
33 ÷ 3 = 11
Step 3: Now, the remainder is 11 which is a prime number.
So, the factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66.
Factor tree
The Pictorial representation of factors of a number. It is in the form of a tree where the given number is split into branches which represent all the factors.
The factor tree of 66:
Factor pair
A pair of factors of a number. The product of those numbers is the number itself. Factor pairs can be both positive and negative.
Positive pair factors: (1, 66), (2, 33), (3, 22), (6, 11).
Negative pair factors: (-1, -66), (-2, -33), (-3, -22), (-6, -11).
Common mistakes and how to avoid them in factors of 66
While finding the factors of any numbers, students tend to make mistakes. Mostly they tend to repeat the same error. Here is a list of some common mistakes and the ways to avoid them.
Mistake 1
Errors in division
Kids tend to make errors in division, to avoid it we need to recheck the calculations. And we need to verify the answer
Factors of 66 examples
Problem 1
The teacher has 33 black pens and 66 blue pens. She wants to give her students both pens together. How many sets of equal-color pens can she make?
The teacher can make 33 sets of equal color pens.
Explanation
Number of black pens = 33
Number of blue pens = 66
First, let’s find the greatest common factor of 66 and 33
Factors of 33 = 1, 3, 11, 33
Factors of 66 = 1, 2, 3, 6, 11, 22, 33, 66
Common factors of 66 are 1, 3, 11, 33
Therefore, the greatest common factor is 33.
So, the total number of sets is 33
Total set of each pen = total number of pens ÷ total number of set
Total black pen set = 33 ÷ 33 = 1
Total blue pen set = 66 ÷ 33 = 2
Hence, the teacher can make 33 sets of pens, which have 1 black pen and 2 blue pens.
Problem 2
what is the LCM of 66 and 195
The LCM of 66 and 195 is 4290.
Explanation
The LCM of two numbers is the product of the highest power of prime factors of each number.
The prime factors of 66 are 21 × 31 × 111
The prime factors of 195 are 31 × 51 × 131
LCM of 66 and 195 = 21 × 31 × 51 × 111 × 131
= 2 × 3 × 5 × 11 × 13 = 4290.
Problem 3
What is the GCF of 66 and 110?
The GCF of 66 and 100 is 20
Explanation
The GCF of two numbers is the product of the prime factor of both the numbers.
Prime factor of 66 is 21 × 31 × 111
Prime factor of 110 is 21 × 51 × 111
Here, the common prime factors are 21 × 111
Therefore, GCF is 21 × 111 = 2 × 11 = 22
Problem 4
List the common factors of 66 and 99
The common factors of 66 and 99 are 1, 3, 11, 33.
Explanation
To find the common factor of two numbers, we need to find the factors and list the common factors.
Factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66
Factors of 99 are 1, 3, 9, 11, 33, 99
Here the common factors are 1, 3, 11, 33
FAQs on factors of 66
1.What is a factor tree of 66?
2.What two numbers make 66?
3.What are the multiples of 66?
4.Is 66 a multiple of 22?
5.What are the prime factors of 66?
6.How can children in Philippines use numbers in everyday life to understand Factors of 66?
7.What are some fun ways kids in Philippines can practice Factors of 66 with numbers?
8.What role do numbers and Factors of 66 play in helping children in Philippines develop problem-solving skills?
9.How can families in Philippines create number-rich environments to improve Factors of 66 skills?
Important glossaries for factors of 66
- Prime number: Any numbers which has only two factors are the prime numbers
- Composite numbers: The number which has more than two factors
- Remainder: The value left after dividing a number by another number. For example, 1 is the remainder when we divide 5 by 2.
- Product: The product of any number is the result of multiplying the number.
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About BrightChamps in Philippines
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.
