Highest Common Factor of 189, 135, 137 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, 135, 137 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 189, 135, 137 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, 135, 137 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, 135, 137 is 1.
HCF(189, 135, 137) = 1
HCF of 189, 135, 137 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, 135, 137 is 1.
Highest Common Factor of 189,135,137 is 1
Step 1: Since 189 > 135, we apply the division lemma to 189 and 135, to get
189 = 135 x 1 + 54
Step 2: Since the reminder 135 ≠ 0, we apply division lemma to 54 and 135, to get
135 = 54 x 2 + 27
Step 3: We consider the new divisor 54 and the new remainder 27, and apply the division lemma to get
54 = 27 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 27, the HCF of 189 and 135 is 27
Notice that 27 = HCF(54,27) = HCF(135,54) = HCF(189,135) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 137 > 27, we apply the division lemma to 137 and 27, to get
137 = 27 x 5 + 2
Step 2: Since the reminder 27 ≠ 0, we apply division lemma to 2 and 27, to get
27 = 2 x 13 + 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 27 and 137 is 1
Notice that 1 = HCF(2,1) = HCF(27,2) = HCF(137,27) .
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Frequently Asked Questions on HCF of 189, 135, 137 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, 135, 137?
Answer: HCF of 189, 135, 137 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 189, 135, 137 using Euclid's Algorithm?
Answer: For arbitrary numbers 189, 135, 137 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.