The HCF of 108, 288 and 360 is 36. HCF of 108, 288 and 360 is the greatest integer that can divide these numbers evenly. HCF stands for Highest Common Factor. For a given set of numbers, there would be common factors, and as the name suggests, the highest among the common factors is known as the HCF. In the given set of numbers 108, 288 and 360, the common factors are 1, 2, 3, 4, 6, 9, 12, 18 and 36. Since 36 is the highest among the common factors, HCF would be 36 for 108, 288 and 360. HCF is also termed GCF, which is the Greatest Common Factor. Learn more on GCF.
What is the HCF of 108, 288 and 360?
The Highest Common Factor, also known as the Greatest Common Factor, of 108, 288 and 360 is 36.
How to Find HCF of 108, 288 and 360?
There are three methods to find the HCF of 108, 288 and 360:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 108, 288 and 360 by Prime Factorisation Method
In the prime factorisation method, the numbers can be expressed as the product of prime numbers. Here, 108, 288 and 360 can be expressed as:
108 = 2 × 2 × 3 × 3 × 3
288 = 2 × 2 × 2 × 2 × 2 × 3 × 3
360 = 2 × 2 × 2 × 3 × 3 × 5
Common prime factors of 108, 288 and 360 are 2, 2, 3 and 3. Therefore, HCF will be,
HCF (108, 288 and 360) = 2 × 2 × 3 × 3 = 36.
HCF of 108, 288 and 360 by Long Division Method
In the long division method, the below steps are followed.
- Choose two numbers from the given set of numbers (Usually, the first two numbers are selected).
- From the chosen numbers, the smallest number becomes the divisor, and the larger number becomes the dividend.
- In the next step, the smaller number becomes the dividend, and the remainder becomes the divisor.
- The above step is followed until the remainder is zero.
- The last divisor would be the HCF.
- The HCF and the left-out number are taken for a new long division.
- HCF becomes the divisor, and the other number becomes the dividend.
- Long division is continued until the remainder becomes zero.
- The last divisor is the HCF of all three numbers.
The HCF of 108, 288 and 360 by long division method is:
Stage 1: Choosing 108 and 288 for 1st Long Division. HCF of 108 and 288 is 36.
Stage 2: Choosing HCF and next number for Long Division.
i.e. HCF from the previous Long Division = 36, and the left-out number is 360. Therefore, HCF is 36.
Therefore, HCF of (108, 288 and 360) = 36
HCF of 108, 288 and 360 by Listing Common Factors
By listing all the factors of given numbers, we can identify the Highest/Greatest/Biggest common factor, which is the HCF. Below is the list of factors for 108, 288 and 360:
Factors of 108:
1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108.
Factors of 288:
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96,144, 288.
Factors of 360:
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360.
Therefore, HCF (108, 288 and 360) = 36
Related Articles
Video Lesson on Properties of HCF and LCM
Solved Examples
1. Find the greatest number that divides 108 and 360 evenly.
The greatest number that divides 108 and 360 is nothing but the GCF, which is 36.
2. What is the second HCF for 108, 288 and 360?
The second HCF for 108, 288 and 360 is 18.
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