Highest Common Factor of 438, 338 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 438, 338 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 438, 338 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 438, 338 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 438, 338 is 2.
HCF(438, 338) = 2
HCF of 438, 338 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 438, 338 is 2.
Highest Common Factor of 438,338 is 2
Step 1: Since 438 > 338, we apply the division lemma to 438 and 338, to get
438 = 338 x 1 + 100
Step 2: Since the reminder 338 ≠ 0, we apply division lemma to 100 and 338, to get
338 = 100 x 3 + 38
Step 3: We consider the new divisor 100 and the new remainder 38, and apply the division lemma to get
100 = 38 x 2 + 24
We consider the new divisor 38 and the new remainder 24,and apply the division lemma to get
38 = 24 x 1 + 14
We consider the new divisor 24 and the new remainder 14,and apply the division lemma to get
24 = 14 x 1 + 10
We consider the new divisor 14 and the new remainder 10,and apply the division lemma to get
14 = 10 x 1 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 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 438 and 338 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(24,14) = HCF(38,24) = HCF(100,38) = HCF(338,100) = HCF(438,338) .
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Frequently Asked Questions on HCF of 438, 338 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 438, 338?
Answer: HCF of 438, 338 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 438, 338 using Euclid's Algorithm?
Answer: For arbitrary numbers 438, 338 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.