Highest Common Factor of 828, 442, 31 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, 442, 31 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 828, 442, 31 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, 442, 31 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, 442, 31 is 1.
HCF(828, 442, 31) = 1
HCF of 828, 442, 31 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, 442, 31 is 1.
Highest Common Factor of 828,442,31 is 1
Step 1: Since 828 > 442, we apply the division lemma to 828 and 442, to get
828 = 442 x 1 + 386
Step 2: Since the reminder 442 ≠ 0, we apply division lemma to 386 and 442, to get
442 = 386 x 1 + 56
Step 3: We consider the new divisor 386 and the new remainder 56, and apply the division lemma to get
386 = 56 x 6 + 50
We consider the new divisor 56 and the new remainder 50,and apply the division lemma to get
56 = 50 x 1 + 6
We consider the new divisor 50 and the new remainder 6,and apply the division lemma to get
50 = 6 x 8 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 828 and 442 is 2
Notice that 2 = HCF(6,2) = HCF(50,6) = HCF(56,50) = HCF(386,56) = HCF(442,386) = HCF(828,442) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 31 > 2, we apply the division lemma to 31 and 2, to get
31 = 2 x 15 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 31 is 1
Notice that 1 = HCF(2,1) = HCF(31,2) .
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Frequently Asked Questions on HCF of 828, 442, 31 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, 442, 31?
Answer: HCF of 828, 442, 31 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 828, 442, 31 using Euclid's Algorithm?
Answer: For arbitrary numbers 828, 442, 31 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.