Highest Common Factor of 1029, 1650 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 1029, 1650 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 1029, 1650 is 3 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 1029, 1650 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 1029, 1650 is 3.
HCF(1029, 1650) = 3
HCF of 1029, 1650 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1029, 1650 is 3.
Highest Common Factor of 1029,1650 is 3
Step 1: Since 1650 > 1029, we apply the division lemma to 1650 and 1029, to get
1650 = 1029 x 1 + 621
Step 2: Since the reminder 1029 ≠ 0, we apply division lemma to 621 and 1029, to get
1029 = 621 x 1 + 408
Step 3: We consider the new divisor 621 and the new remainder 408, and apply the division lemma to get
621 = 408 x 1 + 213
We consider the new divisor 408 and the new remainder 213,and apply the division lemma to get
408 = 213 x 1 + 195
We consider the new divisor 213 and the new remainder 195,and apply the division lemma to get
213 = 195 x 1 + 18
We consider the new divisor 195 and the new remainder 18,and apply the division lemma to get
195 = 18 x 10 + 15
We consider the new divisor 18 and the new remainder 15,and apply the division lemma to get
18 = 15 x 1 + 3
We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 1029 and 1650 is 3
Notice that 3 = HCF(15,3) = HCF(18,15) = HCF(195,18) = HCF(213,195) = HCF(408,213) = HCF(621,408) = HCF(1029,621) = HCF(1650,1029) .
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Frequently Asked Questions on HCF of 1029, 1650 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 1029, 1650?
Answer: HCF of 1029, 1650 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1029, 1650 using Euclid's Algorithm?
Answer: For arbitrary numbers 1029, 1650 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
