The HCF of 16 and 144 is 16. The listing common factors, prime factorisation, and long division are the three most frequent methods for calculating the HCF of 16 and 144. (1, 2, 4, 8, 16) and (1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144) are the factors of 16 and 144, respectively. The greatest number that can divide 16 and 144 perfectly and without leaving any leftover is the HCF of 16 and 144.
Also read: Highest common factor
What is the HCF of 16 and 144?
The answer to this question is 16. This article shows the HCF of 16 and 144 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 16 and 144?
There are three methods to find the HCF of 16 and 144:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 16 and 144 by Prime Factorisation Method
The prime factorisation of 16 and 144 is given by:
Prime factorisation of 16 = (2 × 2 × 2 × 2)
Prime factorisation of 144 = (2 × 2 × 2 × 2 × 3 × 3)
Hence, the HCF of 16 and 144 is 2 × 2 × 2 × 2 = 16
HCF (16, 144) = 16
HCF of 16 and 144 by Long Division Method
The divisor that we receive when the remainder becomes 0 after executing long division repeatedly is HCF of 16 and 144.
No further division can be done.
Hence, HCF (16, 144) = 16
HCF of 16 and 144 by Listing the Factors
To calculate the HCF of 16 and 144 by listing out the common factors, list the factors as shown below:
Factors of 16: 1, 2, 4, 8, 16
Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
There are 5 common factors of 16 and 144, that are 1, 2, 4, 8, and 16. Therefore, the highest common factor of 16 and 144 is 16.
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HCF of 16 and 144 Solved Example
Find the highest number that divides 16 and 144 exactly.
Solution:
The highest number that divides 16 and 144 exactly is their highest common factor, i.e. HCF of 16 and 144.
⇒ Factors of 16 and 144:
Factors of 16 = 1, 2, 4, 8, 16
Factors of 144 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
Therefore, the HCF of 16 and 144 is 16.
Frequently Asked Questions on HCF of 16 and 144
What is the HCF of 16 and 144?
How to Find the HCF of 16 and 144 by Prime Factorisation?
⇒ Since 2, 2, 2, 2 are common terms in the prime factorization of 16 and 144. Hence, HCF(16, 144) = 2 × 2 × 2 × 2 = 16
What are the Methods to Find HCF of 16 and 144?
By Long Division
By Listing Common Factors
By Prime Factorisation
If the HCF of 144 and 16 is 16, Find its LCM.
Since the HCF of 144 and 16 = 16
⇒ 16 × LCM(144, 16) = 2304
Therefore, LCM = 144
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