Highest Common Factor of 1643, 9672 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 1643, 9672 i.e. 31 the largest integer that leaves a remainder zero for all numbers.
HCF of 1643, 9672 is 31 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 1643, 9672 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 1643, 9672 is 31.
HCF(1643, 9672) = 31
HCF of 1643, 9672 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1643, 9672 is 31.
Highest Common Factor of 1643,9672 is 31
Step 1: Since 9672 > 1643, we apply the division lemma to 9672 and 1643, to get
9672 = 1643 x 5 + 1457
Step 2: Since the reminder 1643 ≠ 0, we apply division lemma to 1457 and 1643, to get
1643 = 1457 x 1 + 186
Step 3: We consider the new divisor 1457 and the new remainder 186, and apply the division lemma to get
1457 = 186 x 7 + 155
We consider the new divisor 186 and the new remainder 155,and apply the division lemma to get
186 = 155 x 1 + 31
We consider the new divisor 155 and the new remainder 31,and apply the division lemma to get
155 = 31 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 31, the HCF of 1643 and 9672 is 31
Notice that 31 = HCF(155,31) = HCF(186,155) = HCF(1457,186) = HCF(1643,1457) = HCF(9672,1643) .
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Frequently Asked Questions on HCF of 1643, 9672 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 1643, 9672?
Answer: HCF of 1643, 9672 is 31 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1643, 9672 using Euclid's Algorithm?
Answer: For arbitrary numbers 1643, 9672 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.