HCF of 45 and 180

The HCF of 45 and 180 is 45. The highest number that divides 45 and 180 perfectly and without leaving any leftover is the HCF of these numbers. The factors of 45 and 180 are, respectively, (1, 3, 5, 9, 15, 45) and (1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 30, 36, 45, 60, 90, 180). The listing common factors, prime factorisation, and long division are the three most frequent methods for calculating the HCF of 45 and 180. 

Also read: Highest common factor

What is the HCF of 45 and 180?

The answer to this question is 45. This article shows the HCF of 45 and 180 using various methods for your reference. The greatest of all their common factors is the Highest Common Factor (HCF) of two or more numbers.

How to Find HCF of 45 and 180?

There are three methods to find the HCF of 45 and 180:

  • Prime Factorisation
  • Long Division method
  • Listing common factors

HCF of 45 and 180 by Prime Factorisation Method

The prime factorisation of 45 and 180 is given by:

Prime factorisation of 45 = (3 × 3 × 5)

Prime factorisation of 180 = (2 × 2 × 3 × 3 × 5)

Hence, the HCF of 45 and 180 is 3 × 3 × 5 = 45.

HCF (45, 180) = 45

HCF of 45 and 180 by Long Division Method

The divisor that we receive when the remainder becomes 0 after executing long division repeatedly is HCF of 45 and 180.

HCF of 45 and 180

No further division can be done. 

Hence, HCF (45, 180) = 45

HCF of 45 and 180 by Listing the Factors

To calculate the HCF of 45 and 180 by listing out the common factors, list the factors as shown below:

Factors of 45 = 1, 3, 5, 9, 15, 45

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

Therefore, the HCF of 45 and 180 is 45.

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Video Lesson on Properties of HCF and LCM

HCF of 45 and 180 Solved Example

Find the highest number that divides 45 and 180 exactly.

Solution:

The highest number that divides 45 and 180 exactly is their highest common factor, i.e. HCF of 45 and 180.

⇒ Factors of 45 and 180:

Factors of 45 = 1, 3, 5, 9, 15, 45

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

Therefore, the HCF of 45 and 180 is 45.

Frequently Asked Questions on HCF of 45 and 180

Q1

What is the HCF of 45 and 180?

The HCF of 45 and 180 is 45. To calculate the HCF of 45 and 180, we need to factor each number and choose the highest factor that exactly divides both 45 and 180, i.e., 45.
Q2

How to Find the HCF of 45 and 180 by Prime Factorisation?

To find the HCF of 45 and 180, we will find the prime factorization of the given numbers, i.e. 45 = 3 × 3 × 5; 180 = 2 × 2 × 3 × 3 × 5.
⇒ Since 3, 3, 5 are common terms in the prime factorization of 45 and 180. Hence, HCF(45, 180) = 3 × 3 × 5 = 45
Q3

What are the Methods to Find HCF of 45 and 180?

There are three commonly used methods to find the HCF of 45 and 180.
By Long Division
By Listing Common Factors
By Prime Factorisation
Q4

If the HCF of 180 and 45 is 45, Find its LCM.

HCF(180, 45) × LCM(180, 45) = 180 × 45
Since the HCF of 180 and 45 = 45
⇒ 45 × LCM(180, 45) = 8100
Therefore, LCM = 180
Q5

How to Find the HCF of 45 and 180 by Long Division Method?

To find the HCF of 45, 180 using long division method, 180 is divided by 45. The corresponding divisor (45) when remainder equals 0 is taken as HCF.

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