Highest Common Factor of 828, 123, 536 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 828, 123, 536 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 828, 123, 536 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 828, 123, 536 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 828, 123, 536 is 1.
HCF(828, 123, 536) = 1
HCF of 828, 123, 536 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 828, 123, 536 is 1.
Highest Common Factor of 828,123,536 is 1
Step 1: Since 828 > 123, we apply the division lemma to 828 and 123, to get
828 = 123 x 6 + 90
Step 2: Since the reminder 123 ≠ 0, we apply division lemma to 90 and 123, to get
123 = 90 x 1 + 33
Step 3: We consider the new divisor 90 and the new remainder 33, and apply the division lemma to get
90 = 33 x 2 + 24
We consider the new divisor 33 and the new remainder 24,and apply the division lemma to get
33 = 24 x 1 + 9
We consider the new divisor 24 and the new remainder 9,and apply the division lemma to get
24 = 9 x 2 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 828 and 123 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(24,9) = HCF(33,24) = HCF(90,33) = HCF(123,90) = HCF(828,123) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 536 > 3, we apply the division lemma to 536 and 3, to get
536 = 3 x 178 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: 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 3 and 536 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(536,3) .
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Frequently Asked Questions on HCF of 828, 123, 536 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 828, 123, 536?
Answer: HCF of 828, 123, 536 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 828, 123, 536 using Euclid's Algorithm?
Answer: For arbitrary numbers 828, 123, 536 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.