Common Factors of 135 and 180

The common factors of 135 and 180 are 1, 3, 5, 9, 15, and 45. There are different methods to find the common factors of two or more numbers. Let’s focus on the listing factors method.

Let’s use the listing factors method here. The first step is to list all the factors of 135 and 180 separately. Once the factors of both numbers are listed, we can compare them and identify the common factors.

Step 1: List all the factors

Factors of 135: 1, 3, 5, 9, 15, 27, 45, 135

Factors of 180: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180

Step 2: Compare and identify common factors 1, 3, 5, 9, 15, and 45 are the numbers that appear in both lists of factors.

Therefore, they are the common factors of 135 and 180.

As mentioned earlier, there are different methods to find the common factors. We’ve already seen the listing factors method, and this section discusses the other commonly used methods.

Prime Factorization: For large numbers like 135 and 180, finding the common factors using the listing factors method can be tedious. Hence, we use the prime factorization method, where we find the prime factorization of each number to identify the common prime factors. We then multiply them to get the greatest common factor (GCF).

Venn Diagram: Students who are good at visualization are encouraged to use this method, as it combines prime factorization and visual thinking. The first step is to prime factor each number and place the factors in a Venn diagram. The overlapping section shows the shared primes; multiply them to get the GCF. Now we can find the factors of the GCF to get all the common factors.

Division Ladder Method: The first step is to find all the prime numbers that can divide the given numbers without leaving any remainder. Once we have all the prime numbers, multiply them to get the GCF. We can then find all factors of the GCF to get the common factors.

• Factor – When a number divides another number without leaving a remainder, it is known as a factor of that number.

• Greatest Common Factor (GCF) – The largest number that exactly divides all given numbers.

• Prime Factorization – The method of breaking down a number into the product of prime numbers.

• Divisibility Rules – These rules help verify if a number is a factor of another without actually dividing.

• Listing Factors Method – The method of listing out all factors of all given numbers and comparing them to find the common factors.