The HCF of 90 and 120 is 30. The HCF value divides the numbers 90 and 120 evenly, with zero as the remainder. The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90, and the factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. The methods used to find the HCF i.e. prime factorisation, long division and listing common factors are explained in this article by the experts at BYJU’S with huge experience in the subject.
Also read: Highest common factor
What is the HCF of 90 and 120?
The answer to this question is 30. The methods to find the HCF of 90 and 120 are provided here for the reference of students. The HCF of 90 and 120 is 30, which divides the two given numbers equally.
How to Find HCF of 90 and 120?
The three methods to find HCF of 90 and 120 are:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 90 and 120 by Prime Factorisation Method
The prime factorisation of 90 and 120 is written as:
90 = 2 × 3 × 3 × 5
120 = 2 × 2 × 2 × 3 × 5
The common prime factors of 90 and 120 = 2, 3, 5
Therefore, HCF (90, 120) = 2 × 3 × 5 = 30
HCF of 90 and 120 by Long Division Method
The numbers (90, 120) have to be divided by the prime factors to get the HCF of the numbers. The divisor, when the remainder is zero, is the HCF of 90 and 120.
No further division can be done.
Hence, HCF (90, 120) = 30
HCF of 90 and 120 by Listing Common Factors
Learn how to list the common factors to find the HCF of 90 and 120 here.
Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
There are 9 common factors of 90 and 120, and they are 1, 2, 3, 5, 6, 10, 15 and 30.
Therefore, the highest common factor of 90 and 120 is 30.
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- Prime Factorisation
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Video Lesson on Properties of HCF and LCM
HCF of 90 and 120 Solved Example
Question: Find the LCM if the product of two numbers is 10800 and HCF is 30.
Solution:
Given
Product = 10800
HCF = 30
LCM × HCF = Product
LCM = Product/HCF
LCM = 10800/30
LCM = 360
Hence, the LCM is 360.
Frequently Asked Questions on HCF of 90 and 120
What is the HCF of 90 and 120?
How to find the HCF of 90 and 120 using the long division method?
What methods can be used to determine HCF of 90 and 120?
Determine the HCF of 90 and 120 using prime factorisation.
Using prime factorisation,
90 = 2 × 3 × 3 × 5
120 = 2 × 2 × 2 × 3 × 5
Therefore, the HCF is 30.
Mention the relation between HCF and LCM of 90 and 120.
The relation between HCF and LCM of 90 and 120 is
HCF × LCM = 90 × 120
HCF × LCM = 10800
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