Highest Common Factor of 623, 1734 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 623, 1734 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 623, 1734 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 623, 1734 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 623, 1734 is 1.
HCF(623, 1734) = 1
HCF of 623, 1734 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 623, 1734 is 1.
Highest Common Factor of 623,1734 is 1
Step 1: Since 1734 > 623, we apply the division lemma to 1734 and 623, to get
1734 = 623 x 2 + 488
Step 2: Since the reminder 623 ≠ 0, we apply division lemma to 488 and 623, to get
623 = 488 x 1 + 135
Step 3: We consider the new divisor 488 and the new remainder 135, and apply the division lemma to get
488 = 135 x 3 + 83
We consider the new divisor 135 and the new remainder 83,and apply the division lemma to get
135 = 83 x 1 + 52
We consider the new divisor 83 and the new remainder 52,and apply the division lemma to get
83 = 52 x 1 + 31
We consider the new divisor 52 and the new remainder 31,and apply the division lemma to get
52 = 31 x 1 + 21
We consider the new divisor 31 and the new remainder 21,and apply the division lemma to get
31 = 21 x 1 + 10
We consider the new divisor 21 and the new remainder 10,and apply the division lemma to get
21 = 10 x 2 + 1
We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 623 and 1734 is 1
Notice that 1 = HCF(10,1) = HCF(21,10) = HCF(31,21) = HCF(52,31) = HCF(83,52) = HCF(135,83) = HCF(488,135) = HCF(623,488) = HCF(1734,623) .
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Frequently Asked Questions on HCF of 623, 1734 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 623, 1734?
Answer: HCF of 623, 1734 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 623, 1734 using Euclid's Algorithm?
Answer: For arbitrary numbers 623, 1734 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.