Highest Common Factor of 523, 376 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 523, 376 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 523, 376 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 523, 376 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 523, 376 is 1.
HCF(523, 376) = 1
HCF of 523, 376 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 523, 376 is 1.
Highest Common Factor of 523,376 is 1
Step 1: Since 523 > 376, we apply the division lemma to 523 and 376, to get
523 = 376 x 1 + 147
Step 2: Since the reminder 376 ≠ 0, we apply division lemma to 147 and 376, to get
376 = 147 x 2 + 82
Step 3: We consider the new divisor 147 and the new remainder 82, and apply the division lemma to get
147 = 82 x 1 + 65
We consider the new divisor 82 and the new remainder 65,and apply the division lemma to get
82 = 65 x 1 + 17
We consider the new divisor 65 and the new remainder 17,and apply the division lemma to get
65 = 17 x 3 + 14
We consider the new divisor 17 and the new remainder 14,and apply the division lemma to get
17 = 14 x 1 + 3
We consider the new divisor 14 and the new remainder 3,and apply the division lemma to get
14 = 3 x 4 + 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 523 and 376 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(17,14) = HCF(65,17) = HCF(82,65) = HCF(147,82) = HCF(376,147) = HCF(523,376) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 523, 376 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 523, 376?
Answer: HCF of 523, 376 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 523, 376 using Euclid's Algorithm?
Answer: For arbitrary numbers 523, 376 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.