Highest Common Factor of 431, 698, 736 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 431, 698, 736 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 431, 698, 736 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 431, 698, 736 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 431, 698, 736 is 1.
HCF(431, 698, 736) = 1
HCF of 431, 698, 736 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 431, 698, 736 is 1.
Highest Common Factor of 431,698,736 is 1
Step 1: Since 698 > 431, we apply the division lemma to 698 and 431, to get
698 = 431 x 1 + 267
Step 2: Since the reminder 431 ≠ 0, we apply division lemma to 267 and 431, to get
431 = 267 x 1 + 164
Step 3: We consider the new divisor 267 and the new remainder 164, and apply the division lemma to get
267 = 164 x 1 + 103
We consider the new divisor 164 and the new remainder 103,and apply the division lemma to get
164 = 103 x 1 + 61
We consider the new divisor 103 and the new remainder 61,and apply the division lemma to get
103 = 61 x 1 + 42
We consider the new divisor 61 and the new remainder 42,and apply the division lemma to get
61 = 42 x 1 + 19
We consider the new divisor 42 and the new remainder 19,and apply the division lemma to get
42 = 19 x 2 + 4
We consider the new divisor 19 and the new remainder 4,and apply the division lemma to get
19 = 4 x 4 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 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 431 and 698 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(19,4) = HCF(42,19) = HCF(61,42) = HCF(103,61) = HCF(164,103) = HCF(267,164) = HCF(431,267) = HCF(698,431) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 736 > 1, we apply the division lemma to 736 and 1, to get
736 = 1 x 736 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 736 is 1
Notice that 1 = HCF(736,1) .
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Frequently Asked Questions on HCF of 431, 698, 736 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 431, 698, 736?
Answer: HCF of 431, 698, 736 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 431, 698, 736 using Euclid's Algorithm?
Answer: For arbitrary numbers 431, 698, 736 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.