Highest Common Factor of 714, 296, 161 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 714, 296, 161 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 714, 296, 161 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 714, 296, 161 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 714, 296, 161 is 1.
HCF(714, 296, 161) = 1
HCF of 714, 296, 161 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 714, 296, 161 is 1.
Highest Common Factor of 714,296,161 is 1
Step 1: Since 714 > 296, we apply the division lemma to 714 and 296, to get
714 = 296 x 2 + 122
Step 2: Since the reminder 296 ≠ 0, we apply division lemma to 122 and 296, to get
296 = 122 x 2 + 52
Step 3: We consider the new divisor 122 and the new remainder 52, and apply the division lemma to get
122 = 52 x 2 + 18
We consider the new divisor 52 and the new remainder 18,and apply the division lemma to get
52 = 18 x 2 + 16
We consider the new divisor 18 and the new remainder 16,and apply the division lemma to get
18 = 16 x 1 + 2
We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 714 and 296 is 2
Notice that 2 = HCF(16,2) = HCF(18,16) = HCF(52,18) = HCF(122,52) = HCF(296,122) = HCF(714,296) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 161 > 2, we apply the division lemma to 161 and 2, to get
161 = 2 x 80 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 161 is 1
Notice that 1 = HCF(2,1) = HCF(161,2) .
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Frequently Asked Questions on HCF of 714, 296, 161 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 714, 296, 161?
Answer: HCF of 714, 296, 161 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 714, 296, 161 using Euclid's Algorithm?
Answer: For arbitrary numbers 714, 296, 161 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.