Highest Common Factor of 418, 532, 412 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 418, 532, 412 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 418, 532, 412 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 418, 532, 412 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 418, 532, 412 is 2.
HCF(418, 532, 412) = 2
HCF of 418, 532, 412 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 418, 532, 412 is 2.
Highest Common Factor of 418,532,412 is 2
Step 1: Since 532 > 418, we apply the division lemma to 532 and 418, to get
532 = 418 x 1 + 114
Step 2: Since the reminder 418 ≠ 0, we apply division lemma to 114 and 418, to get
418 = 114 x 3 + 76
Step 3: We consider the new divisor 114 and the new remainder 76, and apply the division lemma to get
114 = 76 x 1 + 38
We consider the new divisor 76 and the new remainder 38, and apply the division lemma to get
76 = 38 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 38, the HCF of 418 and 532 is 38
Notice that 38 = HCF(76,38) = HCF(114,76) = HCF(418,114) = HCF(532,418) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 412 > 38, we apply the division lemma to 412 and 38, to get
412 = 38 x 10 + 32
Step 2: Since the reminder 38 ≠ 0, we apply division lemma to 32 and 38, to get
38 = 32 x 1 + 6
Step 3: We consider the new divisor 32 and the new remainder 6, and apply the division lemma to get
32 = 6 x 5 + 2
We consider the new divisor 6 and the new remainder 2, and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 38 and 412 is 2
Notice that 2 = HCF(6,2) = HCF(32,6) = HCF(38,32) = HCF(412,38) .
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Frequently Asked Questions on HCF of 418, 532, 412 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 418, 532, 412?
Answer: HCF of 418, 532, 412 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 418, 532, 412 using Euclid's Algorithm?
Answer: For arbitrary numbers 418, 532, 412 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.