The HCF of 70, 105 and 175 is 35. The greatest integer, which can divide 70, 105 and 175 evenly, gives the HCF value. The factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70, the factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105 and the factors of 175 are 1, 5, 7, 25, 35, 175. The methods used to find the HCF are prime factorisation, long division and listing common factors.
What is the HCF of 70, 105 and 175?
The answer to this question is 35. The HCF of 70, 105 and 175 using certain methods are shown in this article in a clear-cut manner. The HCF of 70, 105 and 175 is 35, which divides evenly by 70, 105 and 175.
Also read: Highest common factor
How to Find HCF of 70, 105 and 175?
There are three methods to find the HCF of 70, 105 and 175
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 70, 105 and 175 by Prime Factorisation Method
The prime factorisation of 70, 105 and 175 is given by:
70 = 2 × 5 × 7
105 = 3 × 5 × 7
175 = 5 × 5 × 7
Common prime factors of 70, 105, and 175 = 5, 7
Therefore, HCF (70, 105, 175) = 5 × 7 = 35
HCF of 70, 105 and 175 by Long Division Method
The numbers (70, 105, 175) should be divided by the prime factors to determine the HCF of 70, 105 and 175. The divisor obtained when the remainder is zero after repeated long division is the HCF value.
Step I – Divide 70 and 175
Step II – Divide 105 and 35
No further division can be done.
Hence, HCF (70, 105, 175) = 35
HCF of 70, 105 and 175 by Listing Common Factors
We can calculate the HCF of 70, 105 and 175 by listing the common factors as given below:
Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70
Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105
Factors of 175: 1, 5, 7, 25, 35, 175
There are 4 common factors of 70, 105 and 175, and they are 1, 5, 7 and 35.
Therefore, the highest common factor of 70, 105 and 175 is 35.
Related Articles
- Prime Factorisation Calculator
- Properties of HCF and LCM
- Prime Factorisation and Division Method for HCF and LCM
- Prime Factorisation
- GCD Calculator
Video Lesson on Properties of HCF and LCM
HCF of 70, 105 and 175 Solved Example
Question: Among the numbers, 216, 35, 189, 178, 221, 193, 212, 187, find the HCF of 70, 105 and 175.
Solution:
HCF of 70, 105 and 175 is the number which divides 70, 105 and 175, with zero as the remainder.
The number which satisfies this condition is 35.
Hence, the HCF is 35.
Frequently Asked Questions on HCF of 70, 105 and 175
What is the HCF of 70, 105 and 175?
How can the HCF of 70, 105 and 175 be calculated using the long division method?
List the methods to determine HCF of 70, 105 and 175?
With the help of the prime factorisation method, calculate the HCF of 70, 105 and 175.
With the help of the prime factorisation method,
70 = 2 × 5 × 7
105 = 3 × 5 × 7
175 = 5 × 5 × 7
Therefore, the HCF is 35.
What is the relation between HCF and LCM of 70, 105 and 175?
The relation between HCF and LCM of 70, 105 and 175 is
HCF × LCM = 70 × 105 × 175
HCF × LCM = 1286250
Comments