The HCF of 36 and 90 is 18. The greatest number that divides 36 and 90 perfectly without leaving a remainder is called the HCF of those numbers. The factors of 36 and 90 are 1, 2, 3, 4, 6, 9, 12, 18, 36 and 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 respectively. The three most popular approaches for determining the HCF of 36 and 90 are the listing of common factors, prime factorisation, and long division.
Also read: Highest common factor
What is the HCF of 36 and 90?
The answer to this question is 18. This article shows how to find the HCF of 36 and 90 using various methods for your reference. The greatest of all their common factors is the Highest Common Factor (HCF) of two or more numbers.
How to Find HCF of 36 and 90?
There are three methods to find the HCF of 36 and 90:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 36 and 90 by Prime Factorisation Method
The prime factorisation of 36 and 90 is given by:
Prime factorisation of 36 = ( 2 × 2 × 3 × 3)
Prime factorisation of 90 = (2 × 3 × 3 × 5)
Hence, the HCF of 36 and 90 is 18.
HCF (36, 90) = 18
HCF of 36 and 90 by Long Division Method
The divisor that we get when the remainder is 0 after doing long division repeatedly is the HCF of 36 and 90.
No further division can be done.
Hence, HCF (36, 90) = 18
HCF of 36 and 90 by Listing Common Factors
To calculate the HCF of 36 and 90 by listing common factors, list the factors as shown below:
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
There are 6 common factors of 36 and 90, and they are 1, 2, 3, 6, 9, and 18. Therefore, the Highest Common Factor of 36 and 90 is 18.
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HCF of 36 and 90 Solved Example
Question: Find the highest number that divides 36 and 90 exactly.
Solution:
The highest number that divides 36 and 90 exactly is their Highest Common Factor .i.e HCF of 36 and 90.
Factors of 36 and 90:
Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Therefore, the HCF of 36 and 90 is 18.
Frequently Asked Questions on HCF of 36 and 90
What is the HCF of 36 and 90?
How to find the HCF of 36 and 90 by long division method?
If the HCF of 90 and 36 is 18, find its LCM.
The HCF of 90 and 36 = 18
⇒ 18 × LCM (90, 36) = 3240
Therefore, LCM = 180
How to find the HCF of 36 and 90 by prime factorisation?
⇒ 2, 3, 3 are common factors in the prime factorisation of 36 and 90. Hence, HCF (36, 90) = 2 × 3 × 3 = 18
What are the methods to find HCF of 36 and 90?
Long Division
Listing Common Factors
Prime Factorisation
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