HCF of 135 And 225

The HCF of the number is the highest common factor or the highest number who share a common factor. HCF in short is the highest number that divides all the given numbers equally. Euclid’s algorithm can also be used to find the HCF of a number. 

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Methods to Find the HCF

There are three common methods to find the HCF :

• Listing Factor Method
• Long Division Method
• Prime Factorization Method.

Each method has different steps to follow in order to find the HCF of any number.

HCF of 135 and 225 Using the Listing Factor Method

Steps that should be taken to find the HCF using the listing factor method are:

• Step 1: Find the factors for the given number.
• Step 2: List down the common factors.
• Step 3: The highest common factor is the HCF.

Therefore, the HCF of 135 and 225 using the listing factor method is as given below:
Step 1: Find the factors for the given number.
The factors of 135 = 1, 3, 5, 9, 15, 27, 45, 135
The factors of 225 = 1, 3, 5, 9, 15, 25, 45, 75, 225
Step 2: List down the common factors.
There are around six common factors in both the numbers
The common factors = 1,3,5,9,15 and 45
Step 3: The highest common factor is the HCF.
The highest common factor is 45
Hence, HCF(135,225) = 45.

HCF of 135 and 225 Using the Long Division Method

Dividing the larger number with the smaller number gives the HCF using the long division method. The steps are as follows:
Step 1: Divide the larger number by a smaller number until it reaches zero.
Step 2: The last divisor is the HCF of the number.
Therefore, the HCF of 135 and 225 using the long division method is as given below:
Step 1: Divide the larger number by a smaller number until it reaches zero.

Step 2: The last divisor is the HCF of the number.
The last divisor is 45
Hence, HCF (135,225) = 45.

HCF of 135 and 225 Using the Prime Factorization Method

The steps to find the HCF of a number using prime factorization is listed:

Step 1: Find the prime factors of the given numbers.
Step 2: List the common prime factors.
Step 3: Multiply the common factors.
Therefore, the HCF of 135 and 225 using the prime factorization method is as given below:
Step 1: Find the prime factors of the given numbers.
The prime factor if 135 = 3 × 3 × 3 × 5
The prime factor of 225 = 3 × 3 × 5 × 5
Step 2: List the common prime factors.
The common prime factors = 3×3×5
Step 3: Multiply the common factors
Hence the HCF (135,225) = 45.

Solved Examples: 

Example 1: Find the HCF of 1872 and 1320 using the prime factorization method.
The prime factors of 1872 = 2 × 2 × 2 × 2 × 3 × 3 × 13
The prime factors of 1320 = 2 × 2 × 2 × 3 × 5 × 11
The HCF (1872, 1320) = 24.

Example 2: For the given two numbers if the HCF = 45 and their LCM = 675. If one of their numbers is 135 find another number.
Given:
HCF (x, 135)=45
LCM(x,135)=675
Therefore, LCM×HCF = 135 × (X)
 X = (LCM × HCF) ∕ 135
Hence, 
X = (675 × 45)  ∕ 135
Therefore, X = 225 is the other number.

Example 3: The product of two numbers is 30375. If their HCF is 45, what is their LCM?
LCM×HCF = product of two numbers
LCM = product of two numbers  ∕  HCF
LCM = 30375  ∕  45
Hence LCM = 675. 

Example 4: What is the LCM of 135 and 225 if their HCF =45?
The LCM of 135 and 225 = 675 if their HCF = 45.

Example 5: What is the HCF of 64 and 128?
The factor of 64 = 1, 2, 4, 8, 16, 32, 64
The factor of 128 = 1, 2, 4, 8, 16, 32, 64, 128
HCF (64, 128) = 64

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Frequently Asked Questions (FAQ):

What are the LCM and HCF of 135 and 225?
The LCM (135,225) = 675.
The HCF (135, 225) = 45.

What is the product of LCM and HCF of 135 and 225?
The product of LCM and HCF of 135 and 225 = 30375.

What are the common factors in 135 and 225?
The common factors in both 135 and 225 = 1,3,5,9,15 and 45

Solve 135 and 225 using the long division method to find their HCF.

HCF (135,225) = 45

What are the methods to find the HCF of 135 and 225?
There are three methods to find the HCF of a number they are:
1. Listing Factor Method
2. Long Division Method
3. Prime Factorization Method.

Find the HCF of 135 and 225 using the prime factorization method.
The prime factors of 1872 = 2 × 2 × 2 × 2 × 3 × 3 × 13
The prime factors of 1320 = 2 × 2 × 2 × 3 × 5 × 11
Hence HCF(135,225) = 45

What is HCF?
HCF or the highest common factor is the one that can divide any two or more two numbers equally.