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HCF of 70, 105 and 175

HCF of 70, 105 and 175 is the largest possible number that divides 70, 105 and 175 exactly without any remainder. The factors of 70, 105 and 175 are (1, 2, 5, 7, 10, 14, 35, 70), (1, 3, 5, 7, 15, 21, 35, 105) and (1, 5, 7, 25, 35, 175) respectively. There are 3 commonly used methods to find the HCF of 70, 105 and 175 - prime factorization, long division, and Euclidean algorithm.

1.	HCF of 70, 105 and 175
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 70, 105 and 175?

Answer: HCF of 70, 105 and 175 is 35.

Explanation:

The HCF of three non-zero integers, x(70), y(105) and z(175), is the highest positive integer m(35) that divides x(70), y(105) and z(175) without any remainder.

Methods to Find HCF of 70, 105 and 175

The methods to find the HCF of 70, 105 and 175 are explained below.

Prime Factorization Method
Listing Common Factors
Long Division Method

HCF of 70, 105 and 175 by Prime Factorization

Prime factorization of 70, 105 and 175 is (2 × 5 × 7), (3 × 5 × 7) and (5 × 5 × 7) respectively. As visible, 70, 105 and 175 have common prime factors. Hence, the HCF of 70, 105 and 175 is 5 × 7 = 35.

HCF of 70, 105 and 175 by Listing Common Factors

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, that are 1, 35, 5, and 7. Therefore, the highest common factor of 70, 105 and 175 is 35.

HCF of 70, 105 and 175 by Long Division

HCF of 70, 105 and 175 can be represented as HCF of (HCF of 70, 105) and 175. HCF(70, 105, 175) can be thus calculated by first finding HCF(70, 105) using long division and thereafter using this result with 175 to perform long division again.

Step 1: Divide 105 (larger number) by 70 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (70) by the remainder (35). Repeat this process until the remainder = 0.
⇒ HCF(70, 105) = 35.
Step 3: Now to find the HCF of 35 and 175, we will perform a long division on 175 and 35.
Step 4: For remainder = 0, divisor = 35 ⇒ HCF(35, 175) = 35

Thus, HCF(70, 105, 175) = HCF(HCF(70, 105), 175) = 35.

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HCF of 70, 105 and 175 Examples

Example 1: Calculate the HCF of 70, 105, and 175 using LCM of the given numbers.

Solution:

Prime factorization of 70, 105 and 175 is given as,
- 70 = 2 × 5 × 7
- 105 = 3 × 5 × 7
- 175 = 5 × 5 × 7
LCM(70, 105) = 210, LCM(105, 175) = 525, LCM(175, 70) = 350, LCM(70, 105, 175) = 1050
⇒ HCF(70, 105, 175) = [(70 × 105 × 175) × LCM(70, 105, 175)]/[LCM(70, 105) × LCM (105, 175) × LCM(175, 70)]
⇒ HCF(70, 105, 175) = (1286250 × 1050)/(210 × 525 × 350)
⇒ HCF(70, 105, 175) = 35.
Therefore, the HCF of 70, 105 and 175 is 35.
Example 2: Find the highest number that divides 70, 105, and 175 completely.

Solution:

The highest number that divides 70, 105, and 175 exactly is their highest common factor.
- 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 HCF of 70, 105, and 175 is 35.
∴ The highest number that divides 70, 105, and 175 is 35.
Example 3: Verify the relation between the LCM and HCF of 70, 105 and 175.

Solution:

The relation between the LCM and HCF of 70, 105 and 175 is given as, HCF(70, 105, 175) = [(70 × 105 × 175) × LCM(70, 105, 175)]/[LCM(70, 105) × LCM (105, 175) × LCM(70, 175)]
⇒ Prime factorization of 70, 105 and 175:
- 70 = 2 × 5 × 7
- 105 = 3 × 5 × 7
- 175 = 5 × 5 × 7
∴ LCM of (70, 105), (105, 175), (70, 175), and (70, 105, 175) is 210, 525, 350, and 1050 respectively.
Now, LHS = HCF(70, 105, 175) = 35.
And, RHS = [(70 × 105 × 175) × LCM(70, 105, 175)]/[LCM(70, 105) × LCM (105, 175) × LCM(70, 175)] = [(1286250) × 1050]/[210 × 525 × 350]
LHS = RHS = 35.
Hence verified.

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FAQs on HCF of 70, 105 and 175

What is the HCF of 70, 105 and 175?

The HCF of 70, 105 and 175 is 35. To calculate the HCF (Highest Common Factor) of 70, 105 and 175, we need to factor each number (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) and choose the highest factor that exactly divides 70, 105 and 175, i.e., 35.

Which of the following is HCF of 70, 105 and 175? 35, 216, 178, 189, 193, 221, 187, 212

HCF of 70, 105, 175 will be the number that divides 70, 105, and 175 without leaving any remainder. The only number that satisfies the given condition is 35.

What is the Relation Between LCM and HCF of 70, 105 and 175?

The following equation can be used to express the relation between LCM and HCF of 70, 105 and 175, i.e. HCF(70, 105, 175) = [(70 × 105 × 175) × LCM(70, 105, 175)]/[LCM(70, 105) × LCM (105, 175) × LCM(70, 175)].
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What are the Methods to Find HCF of 70, 105 and 175?

There are three commonly used methods to find the HCF of 70, 105 and 175.

By Euclidean Algorithm
By Prime Factorization
By Long Division

How to Find the HCF of 70, 105 and 175 by Prime Factorization?

To find the HCF of 70, 105 and 175, we will find the prime factorization of given numbers, i.e. 70 = 2 × 5 × 7; 105 = 3 × 5 × 7; 175 = 5 × 5 × 7.
⇒ Since 5, 7 are common terms in the prime factorization of 70, 105 and 175. Hence, HCF(70, 105, 175) = 5 × 7 = 35
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