The Highest Common Factor (HCF) of 70, 105, and 175 is 35. This is the largest number that can evenly divide all three numbers. The factors of 70 include 1, 2, 5, 7, 10, 14, 35, and 70. For 105, the factors are 1, 3, 5, 7, 15, 21, 35, and 105. Lastly, the factors of 175 are 1, 5, 7, 25, 35, and 175. To find the HCF, you can use the prime factorization method, the long division method, or by listing common factors.
HCF of 70, 105 and 175 - Calculation Methods and Solved Examples
Last Updated on Jun 11, 2024
Download As PDF
IMPORTANT LINKS
30 in words
50 in words
70 in words
40 in words
Midpoint Formula
Square Root
45000 in words
Cube Root
1999 in roman numerals
13 in roman numerals
200 in roman numerals
70 in roman numerals
Factors of 27
Factors of 16
Factors of 120
Square Root and Cube Root
Squares and Square roots
Types of Function Graphs
Right Triangle Congruence Theorem
80 in Words
How to Calculate the HCF of 70, 105, and 175?
There are three different methods you can use to calculate the HCF of 70, 105, and 175.
- Prime Factorisation
- Long Division method
- Listing common factors
Finding the HCF of 70, 105, and 175 Using Prime Factorisation
Let's begin by finding the prime factorisation of 70, 105, and 175:
70 = 2 × 5 × 7
105 = 3 × 5 × 7
175 = 5 × 5 × 7
The common prime factors of 70, 105, and 175 are 5 and 7. Hence, the HCF (70, 105, 175) = 5 × 7 = 35.
Finding the HCF of 70, 105, and 175 Using the Long Division Method
To use this method, divide the numbers (70, 105, 175) by the prime factors. The divisor you get 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
As no further division can be done, the HCF (70, 105, 175) = 35.
Finding the HCF of 70, 105, and 175 by Listing Common Factors
Another way to find the HCF of 70, 105, and 175 is by listing the common factors as follows:
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
The four common factors of 70, 105, and 175 are 1, 5, 7, and 35. Therefore, the highest common factor of 70, 105, and 175 is 35.
Example of HCF of 70, 105, and 175
Question: If we have the numbers 216, 35, 189, 178, 221, 193, 212, 187, can you find the HCF of 70, 105, and 175?
Solution:
The HCF of 70, 105, and 175 is the number that can divide 70, 105, and 175, leaving zero as the remainder. The number that satisfies this condition is 35. Therefore, the HCF is 35.
More Articles for Maths
Frequently Asked Questions
What is the HCF of 70, 105 and 175?
The HCF of 70, 105 and 175 is 35.
How can the HCF of 70, 105 and 175 be calculated using the long division method?
To calculate the HCF of 70, 105 and 175 using the long division method, 70 is divided by 175 and the number 105 is divided by the HCF 35. The corresponding divisor (35) when remainder equals 0 is the HCF.
List the methods to determine HCF of 70, 105 and 175?
The methods to determine the HCF of 70, 105 and 175 are Long Division, Listing Common Factors and Prime Factorisation.
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 = 1286250.
Test Series
134k Students
NCERT XI-XII Physics Foundation Pack Mock Test
323 TOTAL TESTS
| 3 Free Tests
- 3 Live Test
- 163 Class XI Chapter Tests
- 157 Class XII Chapter Tests