Highest Common Factor of 442, 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 442, 706 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 442, 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 442, 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 442, 706 is 2.
HCF(442, 706) = 2
HCF of 442, 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 442, 706 is 2.
Highest Common Factor of 442,706 is 2
Step 1: Since 706 > 442, we apply the division lemma to 706 and 442, to get
706 = 442 x 1 + 264
Step 2: Since the reminder 442 ≠ 0, we apply division lemma to 264 and 442, to get
442 = 264 x 1 + 178
Step 3: We consider the new divisor 264 and the new remainder 178, and apply the division lemma to get
264 = 178 x 1 + 86
We consider the new divisor 178 and the new remainder 86,and apply the division lemma to get
178 = 86 x 2 + 6
We consider the new divisor 86 and the new remainder 6,and apply the division lemma to get
86 = 6 x 14 + 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 442 and 706 is 2
Notice that 2 = HCF(6,2) = HCF(86,6) = HCF(178,86) = HCF(264,178) = HCF(442,264) = HCF(706,442) .
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Frequently Asked Questions on HCF of 442, 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 442, 706?
Answer: HCF of 442, 706 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 442, 706 using Euclid's Algorithm?
Answer: For arbitrary numbers 442, 706 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.