Highest Common Factor of 706, 66642 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, 66642 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 706, 66642 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, 66642 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, 66642 is 2.
HCF(706, 66642) = 2
HCF of 706, 66642 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, 66642 is 2.
Highest Common Factor of 706,66642 is 2
Step 1: Since 66642 > 706, we apply the division lemma to 66642 and 706, to get
66642 = 706 x 94 + 278
Step 2: Since the reminder 706 ≠ 0, we apply division lemma to 278 and 706, to get
706 = 278 x 2 + 150
Step 3: We consider the new divisor 278 and the new remainder 150, and apply the division lemma to get
278 = 150 x 1 + 128
We consider the new divisor 150 and the new remainder 128,and apply the division lemma to get
150 = 128 x 1 + 22
We consider the new divisor 128 and the new remainder 22,and apply the division lemma to get
128 = 22 x 5 + 18
We consider the new divisor 22 and the new remainder 18,and apply the division lemma to get
22 = 18 x 1 + 4
We consider the new divisor 18 and the new remainder 4,and apply the division lemma to get
18 = 4 x 4 + 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 706 and 66642 is 2
Notice that 2 = HCF(4,2) = HCF(18,4) = HCF(22,18) = HCF(128,22) = HCF(150,128) = HCF(278,150) = HCF(706,278) = HCF(66642,706) .
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Frequently Asked Questions on HCF of 706, 66642 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, 66642?
Answer: HCF of 706, 66642 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 706, 66642 using Euclid's Algorithm?
Answer: For arbitrary numbers 706, 66642 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.