Highest Common Factor of 1647, 8970 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 1647, 8970 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 1647, 8970 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 1647, 8970 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 1647, 8970 is 3.
HCF(1647, 8970) = 3
HCF of 1647, 8970 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1647, 8970 is 3.
Highest Common Factor of 1647,8970 is 3
Step 1: Since 8970 > 1647, we apply the division lemma to 8970 and 1647, to get
8970 = 1647 x 5 + 735
Step 2: Since the reminder 1647 ≠ 0, we apply division lemma to 735 and 1647, to get
1647 = 735 x 2 + 177
Step 3: We consider the new divisor 735 and the new remainder 177, and apply the division lemma to get
735 = 177 x 4 + 27
We consider the new divisor 177 and the new remainder 27,and apply the division lemma to get
177 = 27 x 6 + 15
We consider the new divisor 27 and the new remainder 15,and apply the division lemma to get
27 = 15 x 1 + 12
We consider the new divisor 15 and the new remainder 12,and apply the division lemma to get
15 = 12 x 1 + 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 1647 and 8970 is 3
Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(27,15) = HCF(177,27) = HCF(735,177) = HCF(1647,735) = HCF(8970,1647) .
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Frequently Asked Questions on HCF of 1647, 8970 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 1647, 8970?
Answer: HCF of 1647, 8970 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1647, 8970 using Euclid's Algorithm?
Answer: For arbitrary numbers 1647, 8970 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.