HCF of 9 and 21

The HCF of 9 and 21 is 3. The greatest number that divides 9 and 21 perfectly, leaving no leftovers, is called the HCF of the numbers 9 and 21. 1, 3, 9 and 1, 3, 7, 21 are the factors of 9 and 21, respectively. Listing common factors, prime factorisation, and long division are the three most frequent methods for calculating the HCF of 9 and 21.

Also read: Highest common factor

What is the HCF of 9 and 21?

The answer to this question is 3. This article shows the HCF of 9 and 21 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 9 and 21?

There are three methods to find the HCF of 9 and 21:

  • Prime Factorisation
  • Long Division method
  • Listing common factors

HCF of 9 and 21 by Prime Factorisation Method

The prime factorisation of 9 and 21 is given by:

Prime factorisation of 9 = (3 × 3)

Prime factorisation of 21 = (3 × 7)

Hence, the HCF of 9 and 21 is 3.

HCF (9, 21) = 3

HCF of 9 and 21 by Long Division Method

The divisor that we receive when the remainder becomes 0 after executing a long division repeatedly is HCF of 9 and 21.

HCF of 9 and 21

No further division can be done.

Hence, HCF (9, 21) = 3

HCF of 9 and 21 by Listing the Factors

To calculate the HCF of 9 and 21 by listing out the common factors, list the factors as shown below:

Factors of 9 = 1, 3, 9

Factors of 21 = 1, 3, 7, 21

Therefore, the HCF of 9 and 21 is 3.

Related Articles

Video Lesson on Properties of HCF and LCM

HCF of 9 and 21 Solved Example

Find the HCF of 9 and 21, if their LCM is 63.

Solution:

Given

LCM × HCF = 9 × 21

⇒ HCF(9, 21) = (9 × 21)/63 = 3

Therefore, the highest common factor of 9 and 21 is 3.

Frequently Asked Questions on HCF of 9 and 21

Q1

What is the HCF of 9 and 21?

The HCF of 9 and 21 is 3. To calculate the HCF (Highest Common Factor) of 9 and 21, we need to factor each number and choose the highest factor that exactly divides both 9 and 21, i.e., 3.
Q2

How to Find the HCF of 9 and 21 by Prime Factorisation?

To find the HCF of 9 and 21, we will find the prime factorization of the given numbers, i.e. 9 = 3 × 3; 21 = 3 × 7. ⇒ Since 3 is the only common prime factor of 9 and 21. Hence, HCF (9, 21) = 3.
Q3

What are the Methods to Find HCF of 9 and 21?

There are three commonly used methods to find the HCF of 9 and 21. By Long Division By Listing Common Factors By Prime Factorisation
Q4

If the HCF of 21 and 9 is 3, Find its LCM.

HCF(21, 9) × LCM(21, 9) = 21 × 9 Since the HCF of 21 and 9 = 3 ⇒ 3 × LCM(21, 9) = 189 Therefore, LCM = 63
Q5

How to Find the HCF of 9 and 21 by Long Division Method?

To find the HCF of 9, 21 using long division method, 21 is divided by 9. The corresponding divisor (3) when remainder equals 0 is taken as HCF.

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