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 689, 35034 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 689, 35034 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 689, 35034 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 689, 35034 is 1.
HCF(689, 35034) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 689, 35034 is 1.
Step 1: Since 35034 > 689, we apply the division lemma to 35034 and 689, to get
35034 = 689 x 50 + 584
Step 2: Since the reminder 689 ≠ 0, we apply division lemma to 584 and 689, to get
689 = 584 x 1 + 105
Step 3: We consider the new divisor 584 and the new remainder 105, and apply the division lemma to get
584 = 105 x 5 + 59
We consider the new divisor 105 and the new remainder 59,and apply the division lemma to get
105 = 59 x 1 + 46
We consider the new divisor 59 and the new remainder 46,and apply the division lemma to get
59 = 46 x 1 + 13
We consider the new divisor 46 and the new remainder 13,and apply the division lemma to get
46 = 13 x 3 + 7
We consider the new divisor 13 and the new remainder 7,and apply the division lemma to get
13 = 7 x 1 + 6
We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get
7 = 6 x 1 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 689 and 35034 is 1
Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(13,7) = HCF(46,13) = HCF(59,46) = HCF(105,59) = HCF(584,105) = HCF(689,584) = HCF(35034,689) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 689, 35034?
Answer: HCF of 689, 35034 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 689, 35034 using Euclid's Algorithm?
Answer: For arbitrary numbers 689, 35034 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.