Highest Common Factor of 165, 962, 92 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 165, 962, 92 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 165, 962, 92 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 165, 962, 92 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 165, 962, 92 is 1.
HCF(165, 962, 92) = 1
HCF of 165, 962, 92 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 165, 962, 92 is 1.
Highest Common Factor of 165,962,92 is 1
Step 1: Since 962 > 165, we apply the division lemma to 962 and 165, to get
962 = 165 x 5 + 137
Step 2: Since the reminder 165 ≠ 0, we apply division lemma to 137 and 165, to get
165 = 137 x 1 + 28
Step 3: We consider the new divisor 137 and the new remainder 28, and apply the division lemma to get
137 = 28 x 4 + 25
We consider the new divisor 28 and the new remainder 25,and apply the division lemma to get
28 = 25 x 1 + 3
We consider the new divisor 25 and the new remainder 3,and apply the division lemma to get
25 = 3 x 8 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 165 and 962 is 1
Notice that 1 = HCF(3,1) = HCF(25,3) = HCF(28,25) = HCF(137,28) = HCF(165,137) = HCF(962,165) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 92 > 1, we apply the division lemma to 92 and 1, to get
92 = 1 x 92 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 92 is 1
Notice that 1 = HCF(92,1) .
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Frequently Asked Questions on HCF of 165, 962, 92 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 165, 962, 92?
Answer: HCF of 165, 962, 92 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 165, 962, 92 using Euclid's Algorithm?
Answer: For arbitrary numbers 165, 962, 92 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.