Highest Common Factor of 828, 706 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 828, 706 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 828, 706 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 828, 706 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 828, 706 is 2.
HCF(828, 706) = 2
HCF of 828, 706 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 828, 706 is 2.
Highest Common Factor of 828,706 is 2
Step 1: Since 828 > 706, we apply the division lemma to 828 and 706, to get
828 = 706 x 1 + 122
Step 2: Since the reminder 706 ≠ 0, we apply division lemma to 122 and 706, to get
706 = 122 x 5 + 96
Step 3: We consider the new divisor 122 and the new remainder 96, and apply the division lemma to get
122 = 96 x 1 + 26
We consider the new divisor 96 and the new remainder 26,and apply the division lemma to get
96 = 26 x 3 + 18
We consider the new divisor 26 and the new remainder 18,and apply the division lemma to get
26 = 18 x 1 + 8
We consider the new divisor 18 and the new remainder 8,and apply the division lemma to get
18 = 8 x 2 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 828 and 706 is 2
Notice that 2 = HCF(8,2) = HCF(18,8) = HCF(26,18) = HCF(96,26) = HCF(122,96) = HCF(706,122) = HCF(828,706) .
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Frequently Asked Questions on HCF of 828, 706 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 828, 706?
Answer: HCF of 828, 706 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 828, 706 using Euclid's Algorithm?
Answer: For arbitrary numbers 828, 706 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.