Highest Common Factor of 722, 403, 111 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 722, 403, 111 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 722, 403, 111 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 722, 403, 111 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 722, 403, 111 is 1.
HCF(722, 403, 111) = 1
HCF of 722, 403, 111 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 722, 403, 111 is 1.
Highest Common Factor of 722,403,111 is 1
Step 1: Since 722 > 403, we apply the division lemma to 722 and 403, to get
722 = 403 x 1 + 319
Step 2: Since the reminder 403 ≠ 0, we apply division lemma to 319 and 403, to get
403 = 319 x 1 + 84
Step 3: We consider the new divisor 319 and the new remainder 84, and apply the division lemma to get
319 = 84 x 3 + 67
We consider the new divisor 84 and the new remainder 67,and apply the division lemma to get
84 = 67 x 1 + 17
We consider the new divisor 67 and the new remainder 17,and apply the division lemma to get
67 = 17 x 3 + 16
We consider the new divisor 17 and the new remainder 16,and apply the division lemma to get
17 = 16 x 1 + 1
We consider the new divisor 16 and the new remainder 1,and apply the division lemma to get
16 = 1 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 722 and 403 is 1
Notice that 1 = HCF(16,1) = HCF(17,16) = HCF(67,17) = HCF(84,67) = HCF(319,84) = HCF(403,319) = HCF(722,403) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 111 > 1, we apply the division lemma to 111 and 1, to get
111 = 1 x 111 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 111 is 1
Notice that 1 = HCF(111,1) .
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Frequently Asked Questions on HCF of 722, 403, 111 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 722, 403, 111?
Answer: HCF of 722, 403, 111 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 722, 403, 111 using Euclid's Algorithm?
Answer: For arbitrary numbers 722, 403, 111 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.