The HCF of 120 and 150 is 30. The highest number that divides 120 and 150 evenly is defined as the Highest Common Factor (HCF) of 120 and 150. Prime factorisation, long division method and listing common factors are the three methods used to verify the Highest Common Factor of given numbers. Students can refer to the article HCF and improve their skills in solving problems based on HCF with ease. Let us understand the simple steps to find the Highest Common Factor of 120 and 150 in this article.
What is the HCF of 120 and 150?
The answer to this question is 30. The factors of 120 and 150 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 and 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150, respectively. Here, 30 is the Highest Common Factor of 120 and 150.
How to Find HCF of 120 and 150?
There are three methods to find the HCF of 120 and 150:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 120 and 150 by Prime Factorisation Method
In the prime factorisation, we express 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).
120 = 2 × 2 × 2 × 3 × 5
150 = 2 × 3 × 5 × 5
Common prime factors of 120 and 150 are 2, 3 and 5.
Therefore,
HCF of (120, 150) = 2 × 3 × 5 = 30
HCF of 120 and 150 by Long Division Method
In this method, we use the following steps to find the Highest Common Factor of 120 and 150.
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 zero, then make it a new divisor and write the previous divisor as the new dividend. Then perform the division.
Step 3: Repeat this process until we get the remainder equal to zero. The last divisor will be the HCF of the given two numbers.
The HCF of 120 and 150 by the long division method is;
Therefore, HCF (120, 150) = 30
HCF of 120 and 150 by Listing the Factors
Here, we can verify the Highest Common Factor by listing all the factors of given numbers. The factors of 120 and 150 are as follows:
Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
Hence, HCF (120, 150) = 30
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Video Lesson on Properties of HCF and LCM
Solved Examples
1. What is the highest number that divides both 120 and 150 exactly?
Solution: The Highest Common Factor of 120 and 150 is 30. Therefore, 30 is the highest number that divides both 120 and 150 exactly.
2. What is the HCF of 120 and 150 if their LCM is 600?
Solution: Given
LCM = 600
Product of numbers = 864
We know that,
LCM × HCF = 120 × 150
HCF = (120 × 150) / LCM
HCF = (120 × 150) / 600
HCF = 18000 / 600 = 30
Hence, the HCF of 120 and 150 is 30.
Frequently Asked Questions on HCF of 120 and 150
What is the HCF of 120 and 150?
What are the methods used to find the HCF of 120 and 150?
There are three methods to find the HCF of 120 and 150. They are as follows:
Prime Factorisation
Long Division Method
Listing Common Factors
Is the HCF of 120 and 150 the same as the HCF of 30 and 60?
Determine the LCM if the HCF of 120 and 150 is 30.
We know that
HCF × LCM = 120 × 150
Given
HCF = 30
30 × LCM = 120 × 150
LCM = 600
Therefore the LCM is 600
Write the relation between LCM and HCF of 120 and 150.
The equation used to express the relation between LCM and HCF of 120 and 150 is as follow:
HCF × LCM = 120 × 150
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