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HCF of 60 and 75

HCF of 60 and 75 is the largest possible number that divides 60 and 75 exactly without any remainder. The factors of 60 and 75 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 and 1, 3, 5, 15, 25, 75 respectively. There are 3 commonly used methods to find the HCF of 60 and 75 - long division, Euclidean algorithm, and prime factorization.

1. HCF of 60 and 75
2. List of Methods
3. Solved Examples
4. FAQs

What is HCF of 60 and 75?

Answer: HCF of 60 and 75 is 15.

HCF of 60 and 75

Explanation:

The HCF of two non-zero integers, x(60) and y(75), is the highest positive integer m(15) that divides both x(60) and y(75) without any remainder.

Methods to Find HCF of 60 and 75

The methods to find the HCF of 60 and 75 are explained below.

  • Prime Factorization Method
  • Listing Common Factors
  • Using Euclid's Algorithm

HCF of 60 and 75 by Prime Factorization

Prime factorization of 60 and 75 is (2 × 2 × 3 × 5) and (3 × 5 × 5) respectively. As visible, 60 and 75 have common prime factors. Hence, the HCF of 60 and 75 is 3 × 5 = 15.

HCF of 60 and 75 by Listing Common Factors

HCF of 60 and 75 by Listing Common Factors
  • Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
  • Factors of 75: 1, 3, 5, 15, 25, 75

There are 4 common factors of 60 and 75, that are 1, 3, 5, and 15. Therefore, the highest common factor of 60 and 75 is 15.

HCF of 60 and 75 by Euclidean Algorithm

As per the Euclidean Algorithm, HCF(X, Y) = HCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 75 and Y = 60

  • HCF(75, 60) = HCF(60, 75 mod 60) = HCF(60, 15)
  • HCF(60, 15) = HCF(15, 60 mod 15) = HCF(15, 0)
  • HCF(15, 0) = 15 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 60 and 75 is 15.

☛ Also Check:

HCF of 60 and 75 Examples

  1. Example 1: For two numbers, HCF = 15 and LCM = 300. If one number is 60, find the other number.

    Solution:

    Given: HCF (z, 60) = 15 and LCM (z, 60) = 300
    ∵ HCF × LCM = 60 × (z)
    ⇒ z = (HCF × LCM)/60
    ⇒ z = (15 × 300)/60
    ⇒ z = 75
    Therefore, the other number is 75.

  2. Example 2: Find the highest number that divides 60 and 75 exactly.

    Solution:

    The highest number that divides 60 and 75 exactly is their highest common factor, i.e. HCF of 60 and 75.
    ⇒ Factors of 60 and 75:

    • Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
    • Factors of 75 = 1, 3, 5, 15, 25, 75

    Therefore, the HCF of 60 and 75 is 15.

  3. Example 3: Find the HCF of 60 and 75, if their LCM is 300.

    Solution:

    ∵ LCM × HCF = 60 × 75
    ⇒ HCF(60, 75) = (60 × 75)/300 = 15
    Therefore, the highest common factor of 60 and 75 is 15.

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FAQs on HCF of 60 and 75

What is the HCF of 60 and 75?

The HCF of 60 and 75 is 15. To calculate the HCF (Highest Common Factor) of 60 and 75, we need to factor each number (factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60; factors of 75 = 1, 3, 5, 15, 25, 75) and choose the highest factor that exactly divides both 60 and 75, i.e., 15.

What are the Methods to Find HCF of 60 and 75?

There are three commonly used methods to find the HCF of 60 and 75.

  • By Listing Common Factors
  • By Long Division
  • By Prime Factorization

How to Find the HCF of 60 and 75 by Long Division Method?

To find the HCF of 60, 75 using long division method, 75 is divided by 60. The corresponding divisor (15) when remainder equals 0 is taken as HCF.

If the HCF of 75 and 60 is 15, Find its LCM.

HCF(75, 60) × LCM(75, 60) = 75 × 60
Since the HCF of 75 and 60 = 15
⇒ 15 × LCM(75, 60) = 4500
Therefore, LCM = 300
☛ Highest Common Factor Calculator

What is the Relation Between LCM and HCF of 60, 75?

The following equation can be used to express the relation between LCM and HCF of 60 and 75, i.e. HCF × LCM = 60 × 75.

How to Find the HCF of 60 and 75 by Prime Factorization?

To find the HCF of 60 and 75, we will find the prime factorization of the given numbers, i.e. 60 = 2 × 2 × 3 × 5; 75 = 3 × 5 × 5.
⇒ Since 3, 5 are common terms in the prime factorization of 60 and 75. Hence, HCF(60, 75) = 3 × 5 = 15
☛ Prime Numbers

 
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