Highest Common Factor of 1188, 9658, 23376 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 1188, 9658, 23376 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 1188, 9658, 23376 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 1188, 9658, 23376 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 1188, 9658, 23376 is 2.
HCF(1188, 9658, 23376) = 2
HCF of 1188, 9658, 23376 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1188, 9658, 23376 is 2.
Highest Common Factor of 1188,9658,23376 is 2
Step 1: Since 9658 > 1188, we apply the division lemma to 9658 and 1188, to get
9658 = 1188 x 8 + 154
Step 2: Since the reminder 1188 ≠ 0, we apply division lemma to 154 and 1188, to get
1188 = 154 x 7 + 110
Step 3: We consider the new divisor 154 and the new remainder 110, and apply the division lemma to get
154 = 110 x 1 + 44
We consider the new divisor 110 and the new remainder 44,and apply the division lemma to get
110 = 44 x 2 + 22
We consider the new divisor 44 and the new remainder 22,and apply the division lemma to get
44 = 22 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 22, the HCF of 1188 and 9658 is 22
Notice that 22 = HCF(44,22) = HCF(110,44) = HCF(154,110) = HCF(1188,154) = HCF(9658,1188) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 23376 > 22, we apply the division lemma to 23376 and 22, to get
23376 = 22 x 1062 + 12
Step 2: Since the reminder 22 ≠ 0, we apply division lemma to 12 and 22, to get
22 = 12 x 1 + 10
Step 3: We consider the new divisor 12 and the new remainder 10, and apply the division lemma to get
12 = 10 x 1 + 2
We consider the new divisor 10 and the new remainder 2, and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 22 and 23376 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(22,12) = HCF(23376,22) .
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Frequently Asked Questions on HCF of 1188, 9658, 23376 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 1188, 9658, 23376?
Answer: HCF of 1188, 9658, 23376 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1188, 9658, 23376 using Euclid's Algorithm?
Answer: For arbitrary numbers 1188, 9658, 23376 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
