Highest Common Factor of 966, 414, 220 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, 414, 220 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 966, 414, 220 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, 414, 220 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, 414, 220 is 2.
HCF(966, 414, 220) = 2
HCF of 966, 414, 220 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, 414, 220 is 2.
Highest Common Factor of 966,414,220 is 2
Step 1: Since 966 > 414, we apply the division lemma to 966 and 414, to get
966 = 414 x 2 + 138
Step 2: Since the reminder 414 ≠ 0, we apply division lemma to 138 and 414, to get
414 = 138 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 138, the HCF of 966 and 414 is 138
Notice that 138 = HCF(414,138) = HCF(966,414) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 220 > 138, we apply the division lemma to 220 and 138, to get
220 = 138 x 1 + 82
Step 2: Since the reminder 138 ≠ 0, we apply division lemma to 82 and 138, to get
138 = 82 x 1 + 56
Step 3: We consider the new divisor 82 and the new remainder 56, and apply the division lemma to get
82 = 56 x 1 + 26
We consider the new divisor 56 and the new remainder 26,and apply the division lemma to get
56 = 26 x 2 + 4
We consider the new divisor 26 and the new remainder 4,and apply the division lemma to get
26 = 4 x 6 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 138 and 220 is 2
Notice that 2 = HCF(4,2) = HCF(26,4) = HCF(56,26) = HCF(82,56) = HCF(138,82) = HCF(220,138) .
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Frequently Asked Questions on HCF of 966, 414, 220 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, 414, 220?
Answer: HCF of 966, 414, 220 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 966, 414, 220 using Euclid's Algorithm?
Answer: For arbitrary numbers 966, 414, 220 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.