Highest Common Factor of 706, 396 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 706, 396 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 706, 396 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 706, 396 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 706, 396 is 2.
HCF(706, 396) = 2
HCF of 706, 396 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 706, 396 is 2.
Highest Common Factor of 706,396 is 2
Step 1: Since 706 > 396, we apply the division lemma to 706 and 396, to get
706 = 396 x 1 + 310
Step 2: Since the reminder 396 ≠ 0, we apply division lemma to 310 and 396, to get
396 = 310 x 1 + 86
Step 3: We consider the new divisor 310 and the new remainder 86, and apply the division lemma to get
310 = 86 x 3 + 52
We consider the new divisor 86 and the new remainder 52,and apply the division lemma to get
86 = 52 x 1 + 34
We consider the new divisor 52 and the new remainder 34,and apply the division lemma to get
52 = 34 x 1 + 18
We consider the new divisor 34 and the new remainder 18,and apply the division lemma to get
34 = 18 x 1 + 16
We consider the new divisor 18 and the new remainder 16,and apply the division lemma to get
18 = 16 x 1 + 2
We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 706 and 396 is 2
Notice that 2 = HCF(16,2) = HCF(18,16) = HCF(34,18) = HCF(52,34) = HCF(86,52) = HCF(310,86) = HCF(396,310) = HCF(706,396) .
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Frequently Asked Questions on HCF of 706, 396 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 706, 396?
Answer: HCF of 706, 396 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 706, 396 using Euclid's Algorithm?
Answer: For arbitrary numbers 706, 396 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.