Highest Common Factor of 664, 546, 869 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 664, 546, 869 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 664, 546, 869 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 664, 546, 869 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 664, 546, 869 is 1.
HCF(664, 546, 869) = 1
HCF of 664, 546, 869 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 664, 546, 869 is 1.
Highest Common Factor of 664,546,869 is 1
Step 1: Since 664 > 546, we apply the division lemma to 664 and 546, to get
664 = 546 x 1 + 118
Step 2: Since the reminder 546 ≠ 0, we apply division lemma to 118 and 546, to get
546 = 118 x 4 + 74
Step 3: We consider the new divisor 118 and the new remainder 74, and apply the division lemma to get
118 = 74 x 1 + 44
We consider the new divisor 74 and the new remainder 44,and apply the division lemma to get
74 = 44 x 1 + 30
We consider the new divisor 44 and the new remainder 30,and apply the division lemma to get
44 = 30 x 1 + 14
We consider the new divisor 30 and the new remainder 14,and apply the division lemma to get
30 = 14 x 2 + 2
We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 664 and 546 is 2
Notice that 2 = HCF(14,2) = HCF(30,14) = HCF(44,30) = HCF(74,44) = HCF(118,74) = HCF(546,118) = HCF(664,546) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 869 > 2, we apply the division lemma to 869 and 2, to get
869 = 2 x 434 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 869 is 1
Notice that 1 = HCF(2,1) = HCF(869,2) .
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Frequently Asked Questions on HCF of 664, 546, 869 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 664, 546, 869?
Answer: HCF of 664, 546, 869 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 664, 546, 869 using Euclid's Algorithm?
Answer: For arbitrary numbers 664, 546, 869 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.