Highest Common Factor of 370, 966, 23 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 370, 966, 23 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 370, 966, 23 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 370, 966, 23 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 370, 966, 23 is 1.
HCF(370, 966, 23) = 1
HCF of 370, 966, 23 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 370, 966, 23 is 1.
Highest Common Factor of 370,966,23 is 1
Step 1: Since 966 > 370, we apply the division lemma to 966 and 370, to get
966 = 370 x 2 + 226
Step 2: Since the reminder 370 ≠ 0, we apply division lemma to 226 and 370, to get
370 = 226 x 1 + 144
Step 3: We consider the new divisor 226 and the new remainder 144, and apply the division lemma to get
226 = 144 x 1 + 82
We consider the new divisor 144 and the new remainder 82,and apply the division lemma to get
144 = 82 x 1 + 62
We consider the new divisor 82 and the new remainder 62,and apply the division lemma to get
82 = 62 x 1 + 20
We consider the new divisor 62 and the new remainder 20,and apply the division lemma to get
62 = 20 x 3 + 2
We consider the new divisor 20 and the new remainder 2,and apply the division lemma to get
20 = 2 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 370 and 966 is 2
Notice that 2 = HCF(20,2) = HCF(62,20) = HCF(82,62) = HCF(144,82) = HCF(226,144) = HCF(370,226) = HCF(966,370) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 23 > 2, we apply the division lemma to 23 and 2, to get
23 = 2 x 11 + 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 23 is 1
Notice that 1 = HCF(2,1) = HCF(23,2) .
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Frequently Asked Questions on HCF of 370, 966, 23 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 370, 966, 23?
Answer: HCF of 370, 966, 23 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 370, 966, 23 using Euclid's Algorithm?
Answer: For arbitrary numbers 370, 966, 23 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.