Highest Common Factor of 338, 558, 534 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 338, 558, 534 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 338, 558, 534 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 338, 558, 534 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 338, 558, 534 is 2.
HCF(338, 558, 534) = 2
HCF of 338, 558, 534 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 338, 558, 534 is 2.
Highest Common Factor of 338,558,534 is 2
Step 1: Since 558 > 338, we apply the division lemma to 558 and 338, to get
558 = 338 x 1 + 220
Step 2: Since the reminder 338 ≠ 0, we apply division lemma to 220 and 338, to get
338 = 220 x 1 + 118
Step 3: We consider the new divisor 220 and the new remainder 118, and apply the division lemma to get
220 = 118 x 1 + 102
We consider the new divisor 118 and the new remainder 102,and apply the division lemma to get
118 = 102 x 1 + 16
We consider the new divisor 102 and the new remainder 16,and apply the division lemma to get
102 = 16 x 6 + 6
We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get
16 = 6 x 2 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 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 338 and 558 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(102,16) = HCF(118,102) = HCF(220,118) = HCF(338,220) = HCF(558,338) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 534 > 2, we apply the division lemma to 534 and 2, to get
534 = 2 x 267 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 534 is 2
Notice that 2 = HCF(534,2) .
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Frequently Asked Questions on HCF of 338, 558, 534 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 338, 558, 534?
Answer: HCF of 338, 558, 534 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 338, 558, 534 using Euclid's Algorithm?
Answer: For arbitrary numbers 338, 558, 534 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.