Highest Common Factor of 189, 906, 74 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 189, 906, 74 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 189, 906, 74 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 189, 906, 74 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 189, 906, 74 is 1.
HCF(189, 906, 74) = 1
HCF of 189, 906, 74 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 189, 906, 74 is 1.
Highest Common Factor of 189,906,74 is 1
Step 1: Since 906 > 189, we apply the division lemma to 906 and 189, to get
906 = 189 x 4 + 150
Step 2: Since the reminder 189 ≠ 0, we apply division lemma to 150 and 189, to get
189 = 150 x 1 + 39
Step 3: We consider the new divisor 150 and the new remainder 39, and apply the division lemma to get
150 = 39 x 3 + 33
We consider the new divisor 39 and the new remainder 33,and apply the division lemma to get
39 = 33 x 1 + 6
We consider the new divisor 33 and the new remainder 6,and apply the division lemma to get
33 = 6 x 5 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 189 and 906 is 3
Notice that 3 = HCF(6,3) = HCF(33,6) = HCF(39,33) = HCF(150,39) = HCF(189,150) = HCF(906,189) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 74 > 3, we apply the division lemma to 74 and 3, to get
74 = 3 x 24 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma 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 3 and 74 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(74,3) .
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Frequently Asked Questions on HCF of 189, 906, 74 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 189, 906, 74?
Answer: HCF of 189, 906, 74 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 189, 906, 74 using Euclid's Algorithm?
Answer: For arbitrary numbers 189, 906, 74 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.