Highest Common Factor of 888, 823, 357 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 888, 823, 357 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 888, 823, 357 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 888, 823, 357 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 888, 823, 357 is 1.
HCF(888, 823, 357) = 1
HCF of 888, 823, 357 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 888, 823, 357 is 1.
Highest Common Factor of 888,823,357 is 1
Step 1: Since 888 > 823, we apply the division lemma to 888 and 823, to get
888 = 823 x 1 + 65
Step 2: Since the reminder 823 ≠ 0, we apply division lemma to 65 and 823, to get
823 = 65 x 12 + 43
Step 3: We consider the new divisor 65 and the new remainder 43, and apply the division lemma to get
65 = 43 x 1 + 22
We consider the new divisor 43 and the new remainder 22,and apply the division lemma to get
43 = 22 x 1 + 21
We consider the new divisor 22 and the new remainder 21,and apply the division lemma to get
22 = 21 x 1 + 1
We consider the new divisor 21 and the new remainder 1,and apply the division lemma to get
21 = 1 x 21 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 888 and 823 is 1
Notice that 1 = HCF(21,1) = HCF(22,21) = HCF(43,22) = HCF(65,43) = HCF(823,65) = HCF(888,823) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 357 > 1, we apply the division lemma to 357 and 1, to get
357 = 1 x 357 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 357 is 1
Notice that 1 = HCF(357,1) .
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Frequently Asked Questions on HCF of 888, 823, 357 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 888, 823, 357?
Answer: HCF of 888, 823, 357 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 888, 823, 357 using Euclid's Algorithm?
Answer: For arbitrary numbers 888, 823, 357 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.