Highest Common Factor of 966, 372, 440 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, 372, 440 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 966, 372, 440 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, 372, 440 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, 372, 440 is 2.
HCF(966, 372, 440) = 2
HCF of 966, 372, 440 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, 372, 440 is 2.
Highest Common Factor of 966,372,440 is 2
Step 1: Since 966 > 372, we apply the division lemma to 966 and 372, to get
966 = 372 x 2 + 222
Step 2: Since the reminder 372 ≠ 0, we apply division lemma to 222 and 372, to get
372 = 222 x 1 + 150
Step 3: We consider the new divisor 222 and the new remainder 150, and apply the division lemma to get
222 = 150 x 1 + 72
We consider the new divisor 150 and the new remainder 72,and apply the division lemma to get
150 = 72 x 2 + 6
We consider the new divisor 72 and the new remainder 6,and apply the division lemma to get
72 = 6 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 966 and 372 is 6
Notice that 6 = HCF(72,6) = HCF(150,72) = HCF(222,150) = HCF(372,222) = HCF(966,372) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 440 > 6, we apply the division lemma to 440 and 6, to get
440 = 6 x 73 + 2
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 2 and 6, to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6 and 440 is 2
Notice that 2 = HCF(6,2) = HCF(440,6) .
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Frequently Asked Questions on HCF of 966, 372, 440 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, 372, 440?
Answer: HCF of 966, 372, 440 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 966, 372, 440 using Euclid's Algorithm?
Answer: For arbitrary numbers 966, 372, 440 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.