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.
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.
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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.
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