Highest Common Factor of 208, 535, 828 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 208, 535, 828 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 208, 535, 828 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 208, 535, 828 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 208, 535, 828 is 1.
HCF(208, 535, 828) = 1
HCF of 208, 535, 828 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 208, 535, 828 is 1.
Highest Common Factor of 208,535,828 is 1
Step 1: Since 535 > 208, we apply the division lemma to 535 and 208, to get
535 = 208 x 2 + 119
Step 2: Since the reminder 208 ≠ 0, we apply division lemma to 119 and 208, to get
208 = 119 x 1 + 89
Step 3: We consider the new divisor 119 and the new remainder 89, and apply the division lemma to get
119 = 89 x 1 + 30
We consider the new divisor 89 and the new remainder 30,and apply the division lemma to get
89 = 30 x 2 + 29
We consider the new divisor 30 and the new remainder 29,and apply the division lemma to get
30 = 29 x 1 + 1
We consider the new divisor 29 and the new remainder 1,and apply the division lemma to get
29 = 1 x 29 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 208 and 535 is 1
Notice that 1 = HCF(29,1) = HCF(30,29) = HCF(89,30) = HCF(119,89) = HCF(208,119) = HCF(535,208) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 828 > 1, we apply the division lemma to 828 and 1, to get
828 = 1 x 828 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 828 is 1
Notice that 1 = HCF(828,1) .
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Frequently Asked Questions on HCF of 208, 535, 828 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 208, 535, 828?
Answer: HCF of 208, 535, 828 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 208, 535, 828 using Euclid's Algorithm?
Answer: For arbitrary numbers 208, 535, 828 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.