Highest Common Factor of 966, 794, 972 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, 794, 972 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 966, 794, 972 is 2 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, 794, 972 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, 794, 972 is 2.
HCF(966, 794, 972) = 2
HCF of 966, 794, 972 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, 794, 972 is 2.
Highest Common Factor of 966,794,972 is 2
Step 1: Since 966 > 794, we apply the division lemma to 966 and 794, to get
966 = 794 x 1 + 172
Step 2: Since the reminder 794 ≠ 0, we apply division lemma to 172 and 794, to get
794 = 172 x 4 + 106
Step 3: We consider the new divisor 172 and the new remainder 106, and apply the division lemma to get
172 = 106 x 1 + 66
We consider the new divisor 106 and the new remainder 66,and apply the division lemma to get
106 = 66 x 1 + 40
We consider the new divisor 66 and the new remainder 40,and apply the division lemma to get
66 = 40 x 1 + 26
We consider the new divisor 40 and the new remainder 26,and apply the division lemma to get
40 = 26 x 1 + 14
We consider the new divisor 26 and the new remainder 14,and apply the division lemma to get
26 = 14 x 1 + 12
We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get
14 = 12 x 1 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 966 and 794 is 2
Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(26,14) = HCF(40,26) = HCF(66,40) = HCF(106,66) = HCF(172,106) = HCF(794,172) = HCF(966,794) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 972 > 2, we apply the division lemma to 972 and 2, to get
972 = 2 x 486 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 972 is 2
Notice that 2 = HCF(972,2) .
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Frequently Asked Questions on HCF of 966, 794, 972 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, 794, 972?
Answer: HCF of 966, 794, 972 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 966, 794, 972 using Euclid's Algorithm?
Answer: For arbitrary numbers 966, 794, 972 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.