Highest Common Factor of 882, 645 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 882, 645 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 882, 645 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 882, 645 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 882, 645 is 3.
HCF(882, 645) = 3
HCF of 882, 645 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 882, 645 is 3.
Highest Common Factor of 882,645 is 3
Step 1: Since 882 > 645, we apply the division lemma to 882 and 645, to get
882 = 645 x 1 + 237
Step 2: Since the reminder 645 ≠ 0, we apply division lemma to 237 and 645, to get
645 = 237 x 2 + 171
Step 3: We consider the new divisor 237 and the new remainder 171, and apply the division lemma to get
237 = 171 x 1 + 66
We consider the new divisor 171 and the new remainder 66,and apply the division lemma to get
171 = 66 x 2 + 39
We consider the new divisor 66 and the new remainder 39,and apply the division lemma to get
66 = 39 x 1 + 27
We consider the new divisor 39 and the new remainder 27,and apply the division lemma to get
39 = 27 x 1 + 12
We consider the new divisor 27 and the new remainder 12,and apply the division lemma to get
27 = 12 x 2 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 882 and 645 is 3
Notice that 3 = HCF(12,3) = HCF(27,12) = HCF(39,27) = HCF(66,39) = HCF(171,66) = HCF(237,171) = HCF(645,237) = HCF(882,645) .
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Frequently Asked Questions on HCF of 882, 645 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 882, 645?
Answer: HCF of 882, 645 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 882, 645 using Euclid's Algorithm?
Answer: For arbitrary numbers 882, 645 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.