HCF of 65 and 117

HCF of 65 and 117: HCF is the Highest Common Factor the greatest common divisor that can divide any two numbers equally. It is the greatest common divisor that can divide any number completely. The two numbers have similar factors or divisors which is the HCF of the given number.

Methods to find HCF:

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

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HCF of 65 and 117 Long Division Method

It is one of the effective methods to find the HCF of any number. The HCF of larger or bigger numbers can be found in a fraction of the time with the long division method. The steps are as follows:

Step 1: The larger number is divided using the smaller number until the zero has arrived.
Step 2: The divisor that is the last is the HCF of the number.
Therefore, the HCF of 65 and 117 using the long division method is as follows:
Step 1: The larger number is divided using the smaller number until the zero has arrived.

Step 2: The divisor that is the last is the HCF of the number.
The last divisor here is 13.
Hence, HCF (65,117) = 13.

HCF of 65 and 117 Using the Prime Factorization Method

The prime factorization method to find the HCF of the number follows the listed steps.

Step 1: Find the prime factors of the following steps
Step 2: List down the common prime factor 
Step 3. Multiply the common factors, it is the HCF of the given numbers.
Therefore, the HCF of 65 and 117 using the prime factorization method is as follows:
Step 1: Find the prime factors of the following steps.
The prime factor of 65 = 5 × 13
The prime factor of 117 = 3 × 3 × 13
Step 2: List down the common prime factor 
The common factor in 65 and 117 = 13
Step 3. Multiply the common factors, it is the HCF of the given numbers.
In this case, 13 is the only common prime factor hence there need not be any multiplication.
Therefore the HCF (65,117) = 13

HCF of 65 and 117 Using the Listing Factor Method

There are numbers that have common factors, hence by finding the common factor the HCF of the number is determined.

Step 1: Find the factors.
Step 2: List the common factors.
Step 3: The highest common factor is the HCF of the number.
Therefore, the HCF of 65,117 using the listing factor method is as follows:
Step 1: Find the factors.
The factor of 65 = 1, 5, 13, 65
The factor of 117 = 1, 3, 9, 13, 39, 117
Step 2: List the common factors.
The common factors are 1 and 13
Step 3: The highest common factor is the HCF of the number.
Hence the HCF (65,117) = 13.

Solved Examples

Example 1: What is the greatest common divisor for 65 and 117?
The greatest common divisor of 65 and 117 = 13

Example 2: Find the LCM of 65 and 117 if their HCF is 13.
The LCM of 65 and 117 = 585

Example 3: For two numbers if their HCF =13 and their LCM = 585. If one number is 65 find the other number.
Given:
HCF (x, 65) = 13
LCM(x,65) = 585
Therefore, LCM×HCF = 65× (X)
 X = (LCM × HCF) ∕ 65
Hence, 
X = (13 × 585)  ∕ 65
Therefore, X = 117 is the other number.

Example 4: Find the HCF of 117and 65 using the prime factorization method 
The common prime factor = 13.
Hence HCF(117,65) = 13.

Example 5: The product of the two numbers is 7605. If their HCF is 13, what is their LCM?
LCM×HCF = product of two numbers
LCM = product of two numbers  ∕  HCF
LCM = 7605  ∕  15
Hence LCM = 585.

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Frequently Asked Question (FAQ)

What is the LCM of 65 and 117?
The LCM (65,117) = 585

What is the HCF of 65 and 117?
The HCF (65,117) = 13.

What are the common factors of 65 and 117?
The common factors of 65 and 117 are 1 and 13.

What is the product of 65 and 117?
The product of 65 and 117 = 7605.

What is the HCF of 0 and 2?
The HCF (0,2) = 2

Is HCF and the LCM of two numbers the same?
No, the LCM and HCF of the two numbers are not the same. The LCM is usually higher than the HCF.

Find the highest common divisor between 65 and 117.
The HCD (65,117) = 13.