Highest Common Factor of 704, 869, 218 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 704, 869, 218 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 704, 869, 218 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 704, 869, 218 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 704, 869, 218 is 1.
HCF(704, 869, 218) = 1
HCF of 704, 869, 218 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 704, 869, 218 is 1.
Highest Common Factor of 704,869,218 is 1
Step 1: Since 869 > 704, we apply the division lemma to 869 and 704, to get
869 = 704 x 1 + 165
Step 2: Since the reminder 704 ≠ 0, we apply division lemma to 165 and 704, to get
704 = 165 x 4 + 44
Step 3: We consider the new divisor 165 and the new remainder 44, and apply the division lemma to get
165 = 44 x 3 + 33
We consider the new divisor 44 and the new remainder 33,and apply the division lemma to get
44 = 33 x 1 + 11
We consider the new divisor 33 and the new remainder 11,and apply the division lemma to get
33 = 11 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 704 and 869 is 11
Notice that 11 = HCF(33,11) = HCF(44,33) = HCF(165,44) = HCF(704,165) = HCF(869,704) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 218 > 11, we apply the division lemma to 218 and 11, to get
218 = 11 x 19 + 9
Step 2: Since the reminder 11 ≠ 0, we apply division lemma to 9 and 11, to get
11 = 9 x 1 + 2
Step 3: We consider the new divisor 9 and the new remainder 2, and apply the division lemma to get
9 = 2 x 4 + 1
We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 11 and 218 is 1
Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(11,9) = HCF(218,11) .
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Frequently Asked Questions on HCF of 704, 869, 218 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 704, 869, 218?
Answer: HCF of 704, 869, 218 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 704, 869, 218 using Euclid's Algorithm?
Answer: For arbitrary numbers 704, 869, 218 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
