Highest Common Factor of 858, 528, 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 858, 528, 828 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 858, 528, 828 is 6 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 858, 528, 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 858, 528, 828 is 6.
HCF(858, 528, 828) = 6
HCF of 858, 528, 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 858, 528, 828 is 6.
Highest Common Factor of 858,528,828 is 6
Step 1: Since 858 > 528, we apply the division lemma to 858 and 528, to get
858 = 528 x 1 + 330
Step 2: Since the reminder 528 ≠ 0, we apply division lemma to 330 and 528, to get
528 = 330 x 1 + 198
Step 3: We consider the new divisor 330 and the new remainder 198, and apply the division lemma to get
330 = 198 x 1 + 132
We consider the new divisor 198 and the new remainder 132,and apply the division lemma to get
198 = 132 x 1 + 66
We consider the new divisor 132 and the new remainder 66,and apply the division lemma to get
132 = 66 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 66, the HCF of 858 and 528 is 66
Notice that 66 = HCF(132,66) = HCF(198,132) = HCF(330,198) = HCF(528,330) = HCF(858,528) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 828 > 66, we apply the division lemma to 828 and 66, to get
828 = 66 x 12 + 36
Step 2: Since the reminder 66 ≠ 0, we apply division lemma to 36 and 66, to get
66 = 36 x 1 + 30
Step 3: We consider the new divisor 36 and the new remainder 30, and apply the division lemma to get
36 = 30 x 1 + 6
We consider the new divisor 30 and the new remainder 6, and apply the division lemma to get
30 = 6 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 66 and 828 is 6
Notice that 6 = HCF(30,6) = HCF(36,30) = HCF(66,36) = HCF(828,66) .
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Frequently Asked Questions on HCF of 858, 528, 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 858, 528, 828?
Answer: HCF of 858, 528, 828 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 858, 528, 828 using Euclid's Algorithm?
Answer: For arbitrary numbers 858, 528, 828 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.