Highest Common Factor of 648, 841 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 648, 841 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 648, 841 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 648, 841 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 648, 841 is 1.
HCF(648, 841) = 1
HCF of 648, 841 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 648, 841 is 1.
Highest Common Factor of 648,841 is 1
Step 1: Since 841 > 648, we apply the division lemma to 841 and 648, to get
841 = 648 x 1 + 193
Step 2: Since the reminder 648 ≠ 0, we apply division lemma to 193 and 648, to get
648 = 193 x 3 + 69
Step 3: We consider the new divisor 193 and the new remainder 69, and apply the division lemma to get
193 = 69 x 2 + 55
We consider the new divisor 69 and the new remainder 55,and apply the division lemma to get
69 = 55 x 1 + 14
We consider the new divisor 55 and the new remainder 14,and apply the division lemma to get
55 = 14 x 3 + 13
We consider the new divisor 14 and the new remainder 13,and apply the division lemma to get
14 = 13 x 1 + 1
We consider the new divisor 13 and the new remainder 1,and apply the division lemma to get
13 = 1 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 648 and 841 is 1
Notice that 1 = HCF(13,1) = HCF(14,13) = HCF(55,14) = HCF(69,55) = HCF(193,69) = HCF(648,193) = HCF(841,648) .
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Frequently Asked Questions on HCF of 648, 841 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 648, 841?
Answer: HCF of 648, 841 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 648, 841 using Euclid's Algorithm?
Answer: For arbitrary numbers 648, 841 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.