Highest Common Factor of 966, 670, 531 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 966, 670, 531 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 966, 670, 531 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 966, 670, 531 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 966, 670, 531 is 1.
HCF(966, 670, 531) = 1
HCF of 966, 670, 531 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 966, 670, 531 is 1.
Highest Common Factor of 966,670,531 is 1
Step 1: Since 966 > 670, we apply the division lemma to 966 and 670, to get
966 = 670 x 1 + 296
Step 2: Since the reminder 670 ≠ 0, we apply division lemma to 296 and 670, to get
670 = 296 x 2 + 78
Step 3: We consider the new divisor 296 and the new remainder 78, and apply the division lemma to get
296 = 78 x 3 + 62
We consider the new divisor 78 and the new remainder 62,and apply the division lemma to get
78 = 62 x 1 + 16
We consider the new divisor 62 and the new remainder 16,and apply the division lemma to get
62 = 16 x 3 + 14
We consider the new divisor 16 and the new remainder 14,and apply the division lemma to get
16 = 14 x 1 + 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 966 and 670 is 2
Notice that 2 = HCF(14,2) = HCF(16,14) = HCF(62,16) = HCF(78,62) = HCF(296,78) = HCF(670,296) = HCF(966,670) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 531 > 2, we apply the division lemma to 531 and 2, to get
531 = 2 x 265 + 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 531 is 1
Notice that 1 = HCF(2,1) = HCF(531,2) .
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Frequently Asked Questions on HCF of 966, 670, 531 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 966, 670, 531?
Answer: HCF of 966, 670, 531 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 966, 670, 531 using Euclid's Algorithm?
Answer: For arbitrary numbers 966, 670, 531 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
