Highest Common Factor of 161, 736, 97 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 161, 736, 97 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 161, 736, 97 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 161, 736, 97 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 161, 736, 97 is 1.
HCF(161, 736, 97) = 1
HCF of 161, 736, 97 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 161, 736, 97 is 1.
Highest Common Factor of 161,736,97 is 1
Step 1: Since 736 > 161, we apply the division lemma to 736 and 161, to get
736 = 161 x 4 + 92
Step 2: Since the reminder 161 ≠ 0, we apply division lemma to 92 and 161, to get
161 = 92 x 1 + 69
Step 3: We consider the new divisor 92 and the new remainder 69, and apply the division lemma to get
92 = 69 x 1 + 23
We consider the new divisor 69 and the new remainder 23, and apply the division lemma to get
69 = 23 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 23, the HCF of 161 and 736 is 23
Notice that 23 = HCF(69,23) = HCF(92,69) = HCF(161,92) = HCF(736,161) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 97 > 23, we apply the division lemma to 97 and 23, to get
97 = 23 x 4 + 5
Step 2: Since the reminder 23 ≠ 0, we apply division lemma to 5 and 23, to get
23 = 5 x 4 + 3
Step 3: We consider the new divisor 5 and the new remainder 3, and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
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 23 and 97 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(23,5) = HCF(97,23) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 161, 736, 97 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 161, 736, 97?
Answer: HCF of 161, 736, 97 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 161, 736, 97 using Euclid's Algorithm?
Answer: For arbitrary numbers 161, 736, 97 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.