HCF of 34 and 102

The HCF of 34 and 102 is 34. The highest integer, which divides the two given numbers exactly, is the HCF value. The factors of 34 are 1, 2, 17, 34, and the factors of 102 are 1, 2, 3, 6, 17, 34, 51, 102. Find the HCF value using the methods of prime factorisation, long division and listing common factors, explained in this article by the subject experts at BYJU’S.

What is the HCF of 34 and 102?

The answer to this question is 34. You will learn how to find the HCF of 34 and 102 using various methods in this article. The HCF of 34 and 102 is 34, which divides both 34 and 102 exactly.

Also read: Highest common factor

How to Find HCF of 34 and 102?

There are three methods to find the HCF of 34 and 102

  • Prime Factorisation
  • Long Division method
  • Listing common factors

HCF of 34 and 102 by Prime Factorisation Method

The prime factorisation of 34 and 102 is given by:

34 = 2 × 17

102 = 2 × 3 × 17

Common prime factors of 34 and 102 = 2, 17

Therefore, HCF (34, 102) = 2 × 17 = 34

HCF of 34 and 102 by Long Division Method

To find the HCF, the numbers (34, 102) have to be divided by the prime factors. The HCF of 34 and 102 is the divisor we get when the remainder is zero after repeated long division.

HCF of 34 and 102

No further division can be done.

Hence, HCF (34, 102) = 34

HCF of 34 and 102 by Listing Common Factors

To find the HCF of 34 and 102, the common factors have to be listed as given below:

Factors of 34: 1, 2, 17, 34

Factors of 102: 1, 2, 3, 6, 17, 34, 51, 102

There are 4 common factors of 34 and 102, and they are 1, 2, 17 and 34.

Therefore, the highest common factor of 34 and 102 is 34.

Related Articles

Video Lesson on Properties of HCF and LCM

HCF of 34 and 102 Solved Example

Question: If the product of two numbers = 3468 and HCF = 34, find the LCM.

Solution:

Given

Product of two numbers = 3468

HCF = 34

HCF × LCM = Product of two numbers

34 × LCM = 3468

LCM = 3468/34

LCM = 102

Hence, the LCM is 102.

Frequently Asked Questions on HCF of 34 and 102

Q1

What is the HCF of 34 and 102 if the LCM is 102?

Given

LCM = 102

LCM × HCF = 34 × 102

HCF = (34 × 102)/ 102

HCF = 34

Q2

How can we find the HCF of 34 and 102 using the long division method?

We can find the HCF of 34 and 102 using the long division method, by dividing 102 by 34. The divisor 34 when remainder equals 0 is the HCF.
Q3

Write the methods used to calculate the HCF of 34 and 102.

The methods used to calculate the HCF of 34 and 102 are Long Division, Listing Common Factors and Prime Factorisation.
Q4

What is the HCF of 34 and 102?

The HCF of 34 and 102 is 34.
Q5

Write the relation between HCF and LCM of 34 and 102.

The relation between HCF and LCM of 34 and 102 is

HCF × LCM = 34 × 102

HCF × LCM = 3468

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