Highest Common Factor of 891, 663 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 891, 663 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 891, 663 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 891, 663 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 891, 663 is 3.
HCF(891, 663) = 3
HCF of 891, 663 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 891, 663 is 3.
Highest Common Factor of 891,663 is 3
Step 1: Since 891 > 663, we apply the division lemma to 891 and 663, to get
891 = 663 x 1 + 228
Step 2: Since the reminder 663 ≠ 0, we apply division lemma to 228 and 663, to get
663 = 228 x 2 + 207
Step 3: We consider the new divisor 228 and the new remainder 207, and apply the division lemma to get
228 = 207 x 1 + 21
We consider the new divisor 207 and the new remainder 21,and apply the division lemma to get
207 = 21 x 9 + 18
We consider the new divisor 21 and the new remainder 18,and apply the division lemma to get
21 = 18 x 1 + 3
We consider the new divisor 18 and the new remainder 3,and apply the division lemma to get
18 = 3 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 891 and 663 is 3
Notice that 3 = HCF(18,3) = HCF(21,18) = HCF(207,21) = HCF(228,207) = HCF(663,228) = HCF(891,663) .
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Frequently Asked Questions on HCF of 891, 663 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 891, 663?
Answer: HCF of 891, 663 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 891, 663 using Euclid's Algorithm?
Answer: For arbitrary numbers 891, 663 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.