The HCF of 120 and 168 is 24. HCF of 120 and 168 is the greatest integer that can divide both numbers evenly, and that number is 24. HCF stands for Highest Common Factor, and it is also known as GCF, Greatest Common Factor or GCD, Greatest Common Divisor. For a given set of numbers, there would be multiple common factors, and the highest among the common factors is known as the HCF. For 120 and 168, the common factors are 1, 2, 3, 4, 6, 8, 12 and 24. Since 24 is the highest among the common factors, HCF would be 24 for 120 and 168. You can refer to GCF for more details.
What is the HCF of 120 and 168?
The Highest Common Factor, also known as the Greatest Common Factor, of 120 and 168 is 24.
How to Find HCF of 120 and 168?
There are three methods to find the HCF of 120 and 168:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 120 and 168 by Prime Factorisation Method
In the prime factorisation method, the numbers can be expressed as the product of prime numbers. Here, 120 and 168 can be expressed as:
120 = 2 × 2 × 2 × 3 × 5
168 = 2 × 2 × 2 × 3 × 7
Common prime factors are 2, 2, 2 and 3
Therefore, HCF (120, 168) = 2 × 2 × 2 × 3 = 24.
HCF of 120 and 168 by Long Division Method
In the long division method, the below steps are followed.
- From the given set of 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 of 120 and 168 by long division method is:
Therefore, HCF (120, 168) = 24
HCF of 120 and 168 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 120 and 168:
Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 24, 20, 24, 30, 40, 60, 120
Factors of 168: 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168
Therefore, HCF (120, 168) = 24
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Video Lesson on Properties of HCF and LCM
Solved Examples
1. Find the second greatest number that divides 120 and 168 evenly.
The second greatest number that divides both 120 and 168 evenly is nothing but the second greatest common factor, which is 12.
2. What is the GCF of 24 and 36?
The GCF of 24 and 36 is 12.
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