Highest Common Factor of 659, 1029 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 659, 1029 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 659, 1029 is 1 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 659, 1029 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 659, 1029 is 1.
HCF(659, 1029) = 1
HCF of 659, 1029 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 659, 1029 is 1.
Highest Common Factor of 659,1029 is 1
Step 1: Since 1029 > 659, we apply the division lemma to 1029 and 659, to get
1029 = 659 x 1 + 370
Step 2: Since the reminder 659 ≠ 0, we apply division lemma to 370 and 659, to get
659 = 370 x 1 + 289
Step 3: We consider the new divisor 370 and the new remainder 289, and apply the division lemma to get
370 = 289 x 1 + 81
We consider the new divisor 289 and the new remainder 81,and apply the division lemma to get
289 = 81 x 3 + 46
We consider the new divisor 81 and the new remainder 46,and apply the division lemma to get
81 = 46 x 1 + 35
We consider the new divisor 46 and the new remainder 35,and apply the division lemma to get
46 = 35 x 1 + 11
We consider the new divisor 35 and the new remainder 11,and apply the division lemma to get
35 = 11 x 3 + 2
We consider the new divisor 11 and the new remainder 2,and apply the division lemma to get
11 = 2 x 5 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 659 and 1029 is 1
Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(35,11) = HCF(46,35) = HCF(81,46) = HCF(289,81) = HCF(370,289) = HCF(659,370) = HCF(1029,659) .
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Frequently Asked Questions on HCF of 659, 1029 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 659, 1029?
Answer: HCF of 659, 1029 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 659, 1029 using Euclid's Algorithm?
Answer: For arbitrary numbers 659, 1029 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.