HCF of 3 and 9 | How to Find HCF of 3 and 9 (2024)

The HCF of 3 and 9 is 3. The greatest number that divides 3 and 9 perfectly, leaving no remainder, is known as the HCF of 3 and 9. Listing common factors, prime factorisation, and long division are the three most frequent methods for calculating the HCF of 3 and 9. The factors of 3 and 9 are 1, 3, and 1, 3, 9, respectively.

Also read: Highest common factor

What is the HCF of 3 and 9?

The answer to this question is 3. This article shows how to find the HCF of 3 and 9 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 3 and 9?

There are three methods to find the HCF of 3 and 9:

  • Prime Factorisation
  • Long Division method
  • Listing common factors

HCF of 3 and 9 by Prime Factorisation Method

The prime factorisation of 3 and 9 is given by:

Prime factorisation of 3 = (3)

Prime factorisation of 9 = (3 × 3)

Hence, the HCF of 3 and 9 is 3.

HCF (3, 9) = 3

HCF of 3 and 9 by Long Division Method

The divisor that we get when the remainder is 0 after doing long division repeatedly is the HCF of 3 and 9.

HCF of 3 and 9 | How to Find HCF of 3 and 9 (1)

No further division can be done.

Hence, HCF (3, 9) = 3

HCF of 3 and 9 by Listing Common Factors

To calculate the HCF of 3 and 9 by listing common factors, list the factors as shown below:

Factors of 3: 1, 3

Factors of 9: 1, 3, 9

There are 2 common factors of 3 and 9, and they are 1 and 3. Therefore, the Highest Common Factor of 3 and 9 is 3.

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HCF of 3 and 9 Solved Example

Find the highest number that divides 3 and 9 exactly.

Solution:

The highest number that divides 3 and 9 exactly is their Highest Common Factor .i.e HCF of 3 and 9.

⇒ Factors of 3 and 9:

Factors of 3 = 1, 3

Factors of 9 = 1, 3, 9

Therefore, the HCF of 3 and 9 is 3.

Frequently Asked Questions on HCF of 3 and 9

Q1

What is the HCF of 3 and 9?

The HCF of 3 and 9 is 3. To calculate the HCF (Highest Common Factor) of 3 and 9, we need to factor each number (factors of 3 = 1, 3; factors of 9 = 1, 3, 9) and choose the highest factor that exactly divides both 3 and 9 .i.e 3.

Q2

If the HCF of 9 and 3 is 3, find its LCM.

HCF(9, 3) × LCM(9, 3) = 9 × 3
The HCF of 9 and 3 = 3
⇒ 3 × LCM(9, 3) = 27
Therefore, LCM = 9

Q3

How to find the HCF of 3 and 9 by prime factorisation?

To find the HCF of 3 and 9, we need to find the prime factorisation of the given numbers .i.e 3 = 3; 9 = 3 × 3.
⇒ 3 is the only common prime factor of 3 and 9. Hence, HCF (3, 9) = 3.

Q4

What is the relation between LCM and HCF of 3 and 9?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF (Highest Common Factor) of 3 and 9 .i.e HCF × LCM = 3 × 9.

Q5

What are the methods to find HCF of 3 and 9?

There are three commonly used methods to find the HCF of 3 and 9. They are:
Long Division
Listing Common Factors
Prime Factorisation

HCF of 3 and 9 | How to Find HCF of 3 and 9 (2024)

FAQs

HCF of 3 and 9 | How to Find HCF of 3 and 9? ›

The HCF of 3 and 9 is 3. To calculate the HCF (Highest Common Factor) of 3 and 9, we need to factor each number (factors of 3 = 1, 3; factors of 9 = 1, 3, 9) and choose the highest factor that exactly divides both 3 and 9 . i.e 3.

How to find HCF of two numbers? ›

The highest common factor is found by multiplying all the factors which appear in both lists: So the HCF of 60 and 72 is 2 × 2 × 3 which is 12. The lowest common multiple is found by multiplying all the factors which appear in either list: So the LCM of 60 and 72 is 2 × 2 × 2 × 3 × 3 × 5 which is 360.

What is the LCM of 3 9 and 9? ›

FAQs on LCM of 3 and 9

The LCM of 3 and 9 is 9. To find the least common multiple (LCM) of 3 and 9, we need to find the multiples of 3 and 9 (multiples of 3 = 3, 6, 9, 12; multiples of 9 = 9, 18, 27, 36) and choose the smallest multiple that is exactly divisible by 3 and 9, i.e., 9.

What is the HCF method example? ›

HCF can be evaluated for two or more than two numbers. It is the greatest divisor for any two or more numbers, that can equally or completely divide the given numbers. For Example: The Highest common factor of 60 and 75 is 15 because 15 is the largest number which can divide both 60 and 75 exactly.

How many methods to find HCF? ›

Ans: There are 4 primary methods for finding the HCF and LCM: HCF by Prime Factorisation Method. HCF by Division Method. LCM by Prime Factorisation Method.

What is the formula for HCF and LCM? ›

The formula of HCF and LCM is: Product of two numbers = LCM of two numbers x HCF of two numbers. The following formulas can be deduced from the HCF and LCM Formula. HCF of two numbers = Product of two numbers/ LCM of two numbers.

What is the HCF of 9? ›

Factors of 9 = 1, 3, 9.

What is the rule for HCF? ›

To find the HCF of two or three given numbers, divide the greater number by the smaller one. Then divide the divisor by the remainder. Go on repeating the process of dividing the preceding divisor by the remainder, till zero remainder is obtained. The last divisor'is the HCF of the given numbers.

How do you identify the HCF? ›

Find the prime factors of each of the given number. Next, we identify the common prime factors of the given numbers. We then multiply the common factors. The product of these common factors is the HCF of the given numbers.

What is the most common multiple of 3 and 9? ›

Here is the prime factorization of 3:
  • 3 1 3^1 31. And this is the prime factorization of 9:
  • 3 2 3^2 32. When you compare the prime factorization of these two numbers, you want to look for the highest power that each prime factor is raised to. ...
  • 3 2 = 9 3^2 = 9 32=9. Through this we see that the LCM of 3 and 9 is 9.

What is the HCF of 3 and 8? ›

The Highest Common Factor (HCF) of 3 and 8 is 1, and the Least Common Multiple (LCM) of 3 and 8 is 24.

What is the HCF of 3 and 2? ›

The HCF of 2 and 3 is 1. To calculate the highest common factor of 2 and 3, we need to factor each number (factors of 2 = 1, 2; factors of 3 = 1, 3) and choose the highest factor that exactly divides both 2 and 3, i.e. 1.

What is the HCF of 3 and 6? ›

The only common prime factor of 3 and 6 is 3. Hence, the HCF of 3 and 6 is 3.

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