Highest Common Factor of 336, 538 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 336, 538 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 336, 538 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 336, 538 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 336, 538 is 2.
HCF(336, 538) = 2
HCF of 336, 538 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 336, 538 is 2.
Highest Common Factor of 336,538 is 2
Step 1: Since 538 > 336, we apply the division lemma to 538 and 336, to get
538 = 336 x 1 + 202
Step 2: Since the reminder 336 ≠ 0, we apply division lemma to 202 and 336, to get
336 = 202 x 1 + 134
Step 3: We consider the new divisor 202 and the new remainder 134, and apply the division lemma to get
202 = 134 x 1 + 68
We consider the new divisor 134 and the new remainder 68,and apply the division lemma to get
134 = 68 x 1 + 66
We consider the new divisor 68 and the new remainder 66,and apply the division lemma to get
68 = 66 x 1 + 2
We consider the new divisor 66 and the new remainder 2,and apply the division lemma to get
66 = 2 x 33 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 336 and 538 is 2
Notice that 2 = HCF(66,2) = HCF(68,66) = HCF(134,68) = HCF(202,134) = HCF(336,202) = HCF(538,336) .
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Frequently Asked Questions on HCF of 336, 538 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 336, 538?
Answer: HCF of 336, 538 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 336, 538 using Euclid's Algorithm?
Answer: For arbitrary numbers 336, 538 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.