Highest Common Factor of 670, 823, 182 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 670, 823, 182 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 670, 823, 182 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 670, 823, 182 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 670, 823, 182 is 1.
HCF(670, 823, 182) = 1
HCF of 670, 823, 182 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 670, 823, 182 is 1.
Highest Common Factor of 670,823,182 is 1
Step 1: Since 823 > 670, we apply the division lemma to 823 and 670, to get
823 = 670 x 1 + 153
Step 2: Since the reminder 670 ≠ 0, we apply division lemma to 153 and 670, to get
670 = 153 x 4 + 58
Step 3: We consider the new divisor 153 and the new remainder 58, and apply the division lemma to get
153 = 58 x 2 + 37
We consider the new divisor 58 and the new remainder 37,and apply the division lemma to get
58 = 37 x 1 + 21
We consider the new divisor 37 and the new remainder 21,and apply the division lemma to get
37 = 21 x 1 + 16
We consider the new divisor 21 and the new remainder 16,and apply the division lemma to get
21 = 16 x 1 + 5
We consider the new divisor 16 and the new remainder 5,and apply the division lemma to get
16 = 5 x 3 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 670 and 823 is 1
Notice that 1 = HCF(5,1) = HCF(16,5) = HCF(21,16) = HCF(37,21) = HCF(58,37) = HCF(153,58) = HCF(670,153) = HCF(823,670) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 182 > 1, we apply the division lemma to 182 and 1, to get
182 = 1 x 182 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 182 is 1
Notice that 1 = HCF(182,1) .
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Frequently Asked Questions on HCF of 670, 823, 182 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 670, 823, 182?
Answer: HCF of 670, 823, 182 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 670, 823, 182 using Euclid's Algorithm?
Answer: For arbitrary numbers 670, 823, 182 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.