The HCF of 90 and 105 is 15. The greatest number that divides 90 and 105 exactly and without a remainder is the HCF of these numbers. The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90, and the factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105. Listing common factors, prime factorisation and long division are the three most frequent methods for calculating the HCF of 90 and 105.
Also read: Highest common factor
What is the HCF of 90 and 105?
The answer to this question is 15. This article shows the HCF of 90 and 105 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 90 and 105?
There are three methods to find the HCF of 90 and 105:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 90 and 105 by Prime Factorisation Method
The prime factorisation of 90 and 105 is given by:
Prime factorisation of 90 = (2 × 3 × 3 × 5)
Prime factorisation of 105 = (3 × 5 × 7)
Hence, the HCF of 90 and 105 is 3 × 5 = 15
HCF (90, 105) = 15
HCF of 90 and 105 by Long Division Method
The divisor that we get when the remainder is 0 after doing a long division repeatedly is the HCF of 90 and 105.
No further division can be done.
Hence, HCF (90, 105) = 15
HCF of 90 and 105 by Listing Common Factors
To calculate the HCF of 90 and 105 by listing common factors, list the factors as shown below:
Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105
There are 4 common factors of 90 and 105, and they are 1, 3, 5, and 15. Therefore, the Highest Common Factor of 90 and 105 is 15.
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HCF of 90 and 105 Solved Example
Find the highest number that divides 90 and 105 exactly.
Solution:
The highest number that divides 90 and 105 exactly is their Highest Common Factor, .i.e HCF of 90 and 105.
⇒ Factors of 90 and 105:
Factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Factors of 105 = 1, 3, 5, 7, 15, 21, 35, 105
Therefore, the HCF of 90 and 105 is 15.
Frequently Asked Questions on HCF of 90 and 105
What is the HCF of 90 and 105?
How to find the HCF of 90 and 105 by prime factorisation?
⇒ 3, 5 are common terms in the prime factorisation of 90 and 105. Hence, HCF(90, 105) = 3 × 5 = 15
What are the methods to find the HCF of 90 and 105?
Long Division
Listing Common Factors
Prime Factorisation
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