Highest Common Factor of 170, 218, 334 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 170, 218, 334 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 170, 218, 334 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 170, 218, 334 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 170, 218, 334 is 2.
HCF(170, 218, 334) = 2
HCF of 170, 218, 334 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 170, 218, 334 is 2.
Highest Common Factor of 170,218,334 is 2
Step 1: Since 218 > 170, we apply the division lemma to 218 and 170, to get
218 = 170 x 1 + 48
Step 2: Since the reminder 170 ≠ 0, we apply division lemma to 48 and 170, to get
170 = 48 x 3 + 26
Step 3: We consider the new divisor 48 and the new remainder 26, and apply the division lemma to get
48 = 26 x 1 + 22
We consider the new divisor 26 and the new remainder 22,and apply the division lemma to get
26 = 22 x 1 + 4
We consider the new divisor 22 and the new remainder 4,and apply the division lemma to get
22 = 4 x 5 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 170 and 218 is 2
Notice that 2 = HCF(4,2) = HCF(22,4) = HCF(26,22) = HCF(48,26) = HCF(170,48) = HCF(218,170) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 334 > 2, we apply the division lemma to 334 and 2, to get
334 = 2 x 167 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 334 is 2
Notice that 2 = HCF(334,2) .
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Frequently Asked Questions on HCF of 170, 218, 334 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 170, 218, 334?
Answer: HCF of 170, 218, 334 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 170, 218, 334 using Euclid's Algorithm?
Answer: For arbitrary numbers 170, 218, 334 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.