Highest Common Factor of 900, 380, 966 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 900, 380, 966 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 900, 380, 966 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 900, 380, 966 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 900, 380, 966 is 2.
HCF(900, 380, 966) = 2
HCF of 900, 380, 966 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 900, 380, 966 is 2.
Highest Common Factor of 900,380,966 is 2
Step 1: Since 900 > 380, we apply the division lemma to 900 and 380, to get
900 = 380 x 2 + 140
Step 2: Since the reminder 380 ≠ 0, we apply division lemma to 140 and 380, to get
380 = 140 x 2 + 100
Step 3: We consider the new divisor 140 and the new remainder 100, and apply the division lemma to get
140 = 100 x 1 + 40
We consider the new divisor 100 and the new remainder 40,and apply the division lemma to get
100 = 40 x 2 + 20
We consider the new divisor 40 and the new remainder 20,and apply the division lemma to get
40 = 20 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 900 and 380 is 20
Notice that 20 = HCF(40,20) = HCF(100,40) = HCF(140,100) = HCF(380,140) = HCF(900,380) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 966 > 20, we apply the division lemma to 966 and 20, to get
966 = 20 x 48 + 6
Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 6 and 20, to get
20 = 6 x 3 + 2
Step 3: We consider the new divisor 6 and the new remainder 2, and apply the division lemma 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 20 and 966 is 2
Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(966,20) .
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Frequently Asked Questions on HCF of 900, 380, 966 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 900, 380, 966?
Answer: HCF of 900, 380, 966 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 900, 380, 966 using Euclid's Algorithm?
Answer: For arbitrary numbers 900, 380, 966 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.