Highest Common Factor of 828, 2973, 2355 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, 2973, 2355 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 828, 2973, 2355 is 3 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, 2973, 2355 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, 2973, 2355 is 3.
HCF(828, 2973, 2355) = 3
HCF of 828, 2973, 2355 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, 2973, 2355 is 3.
Highest Common Factor of 828,2973,2355 is 3
Step 1: Since 2973 > 828, we apply the division lemma to 2973 and 828, to get
2973 = 828 x 3 + 489
Step 2: Since the reminder 828 ≠ 0, we apply division lemma to 489 and 828, to get
828 = 489 x 1 + 339
Step 3: We consider the new divisor 489 and the new remainder 339, and apply the division lemma to get
489 = 339 x 1 + 150
We consider the new divisor 339 and the new remainder 150,and apply the division lemma to get
339 = 150 x 2 + 39
We consider the new divisor 150 and the new remainder 39,and apply the division lemma to get
150 = 39 x 3 + 33
We consider the new divisor 39 and the new remainder 33,and apply the division lemma to get
39 = 33 x 1 + 6
We consider the new divisor 33 and the new remainder 6,and apply the division lemma to get
33 = 6 x 5 + 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 2973 is 3
Notice that 3 = HCF(6,3) = HCF(33,6) = HCF(39,33) = HCF(150,39) = HCF(339,150) = HCF(489,339) = HCF(828,489) = HCF(2973,828) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 2355 > 3, we apply the division lemma to 2355 and 3, to get
2355 = 3 x 785 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 2355 is 3
Notice that 3 = HCF(2355,3) .
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Frequently Asked Questions on HCF of 828, 2973, 2355 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, 2973, 2355?
Answer: HCF of 828, 2973, 2355 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 828, 2973, 2355 using Euclid's Algorithm?
Answer: For arbitrary numbers 828, 2973, 2355 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.