Highest Common Factor of 34, 60, 234 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 34, 60, 234 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 34, 60, 234 is 2 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 34, 60, 234 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 34, 60, 234 is 2.
HCF(34, 60, 234) = 2
HCF of 34, 60, 234 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 34, 60, 234 is 2.
Highest Common Factor of 34,60,234 is 2
Step 1: Since 60 > 34, we apply the division lemma to 60 and 34, to get
60 = 34 x 1 + 26
Step 2: Since the reminder 34 ≠ 0, we apply division lemma to 26 and 34, to get
34 = 26 x 1 + 8
Step 3: We consider the new divisor 26 and the new remainder 8, and apply the division lemma to get
26 = 8 x 3 + 2
We consider the new divisor 8 and the new remainder 2, and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 34 and 60 is 2
Notice that 2 = HCF(8,2) = HCF(26,8) = HCF(34,26) = HCF(60,34) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 234 > 2, we apply the division lemma to 234 and 2, to get
234 = 2 x 117 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 234 is 2
Notice that 2 = HCF(234,2) .
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Frequently Asked Questions on HCF of 34, 60, 234 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 34, 60, 234?
Answer: HCF of 34, 60, 234 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 34, 60, 234 using Euclid's Algorithm?
Answer: For arbitrary numbers 34, 60, 234 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.