The HCF of 84 and 144 is 12. HCF is one of the most important concepts in Mathematics. The largest positive integer that divides two or more numbers evenly is defined as the Highest Common Factor (HCF). In the given numbers, 12 is the largest number that divides both 84 and 144 exactly. BYJU’S experts formulated the article HCF in a simple and understandable manner so that students can learn the concept in a better way along with clearing their doubts instantly. In this article, we will discuss the simple steps of how to determine the Highest Common Factor of 84 and 144 in a descriptive manner.
What is the HCF of 84 and 144?
The answer to this question is 12. The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 and the factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144. Here, the highest number common in both factors of 84 and 144 is 12. Hence, the Highest Common Factor of 84 and 144 is 12.
How to Find HCF of 84 and 144?
There are three methods to find the HCF of 84 and 144:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 84 and 144 by Prime Factorisation Method
Here, we write the numbers as the product of prime factors. To find the Highest Common Factor, multiply all the common prime factors with the lowest degree (power).
84 = 2 × 2 × 3 × 7
144 = 2 × 2 × 2 × 2 × 3 × 3
Common prime factors of 84 and 144 are 2, 2 and 3.
Therefore,
HCF of (84, 144) = 2 × 2 × 3 = 12
HCF of 84 and 144 by Long Division Method
The following steps are used to find the Highest Common Factor of 84 and 144:
Step 1: Divide the largest number by the smallest number from the given two numbers.
Step 2: Now, check the remainder. If it is not 0, then make it a new divisor and write the previous divisor as the new dividend. Then perform the division.
Step 3: Continue this process until we get the remainder as zero. The last divisor will be the HCF of the given two numbers.
The HCF of 84 and 144 by the long division method is:
Hence, HCF (84, 144) = 12
HCF of 84 and 144 by Listing the Factors
Here, we can find the Highest Common Factor by listing all the factors of given numbers. The factors of 84 and 144 are as follows:
Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
Hence, HCF (84, 144) = 12
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Video Lesson on Properties of HCF and LCM
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Solved Example
Question: What is the HCF of 84 and 144 if their LCM is 1008?
Solution: We know that
LCM × HCF = 84 × 144
HCF (84, 144) = (84 × 144) / LCM
HCF (84, 144) = (84 × 144) / 1008
HCF (84, 144) = 12096 / 1008 = 12
Hence, the HCF of 84 and 144 is 12.
Frequently Asked Questions on HCF of 84 and 144
What is the HCF of 84 and 144?
What are the methods used to find the HCF of 84 and 144?
There are three methods to find the HCF of 84 and 144. They are as follows:
Prime Factorisation
Long Division Method
Listing Common Factors
Is the HCF of 84 and 144 the same as the HCF of 36 and 84?
What is the LCM if the HCF of 84 and 144 is 12?
We know that
HCF × LCM = 84 × 144
Given
HCF = 12
12 × LCM = 84 × 144
LCM = (84 × 144) / 12
LCM = 1008
Using the prime factorisation method, find the HCF of 84 and 144.
In prime factorisation, we depict the given numbers as the product of prime factors to determine the HCF
84 = 2 × 2 × 3 × 7
144 = 2 × 2 × 2 × 2 × 3 × 3
Common prime factors of 84 and 144 are 2, 2 and 3
HCF of (84, 144) = 2 × 2 × 3 = 12
Therefore, the HCF of 84 and 144 is 12.
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