Highest Common Factor of 906, 534, 197, 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 906, 534, 197, 23 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 906, 534, 197, 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 906, 534, 197, 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 906, 534, 197, 23 is 1.
HCF(906, 534, 197, 23) = 1
HCF of 906, 534, 197, 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 906, 534, 197, 23 is 1.
Highest Common Factor of 906,534,197,23 is 1
Step 1: Since 906 > 534, we apply the division lemma to 906 and 534, to get
906 = 534 x 1 + 372
Step 2: Since the reminder 534 ≠ 0, we apply division lemma to 372 and 534, to get
534 = 372 x 1 + 162
Step 3: We consider the new divisor 372 and the new remainder 162, and apply the division lemma to get
372 = 162 x 2 + 48
We consider the new divisor 162 and the new remainder 48,and apply the division lemma to get
162 = 48 x 3 + 18
We consider the new divisor 48 and the new remainder 18,and apply the division lemma to get
48 = 18 x 2 + 12
We consider the new divisor 18 and the new remainder 12,and apply the division lemma to get
18 = 12 x 1 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 906 and 534 is 6
Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(48,18) = HCF(162,48) = HCF(372,162) = HCF(534,372) = HCF(906,534) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 197 > 6, we apply the division lemma to 197 and 6, to get
197 = 6 x 32 + 5
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 5 and 6, to get
6 = 5 x 1 + 1
Step 3: We consider the new divisor 5 and the new remainder 1, and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6 and 197 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(197,6) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 23 > 1, we apply the division lemma to 23 and 1, to get
23 = 1 x 23 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 23 is 1
Notice that 1 = HCF(23,1) .
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Frequently Asked Questions on HCF of 906, 534, 197, 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 906, 534, 197, 23?
Answer: HCF of 906, 534, 197, 23 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 906, 534, 197, 23 using Euclid's Algorithm?
Answer: For arbitrary numbers 906, 534, 197, 23 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.