Highest Common Factor of 824, 3172 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 824, 3172 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 824, 3172 is 4 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 824, 3172 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 824, 3172 is 4.
HCF(824, 3172) = 4
HCF of 824, 3172 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 824, 3172 is 4.
Highest Common Factor of 824,3172 is 4
Step 1: Since 3172 > 824, we apply the division lemma to 3172 and 824, to get
3172 = 824 x 3 + 700
Step 2: Since the reminder 824 ≠ 0, we apply division lemma to 700 and 824, to get
824 = 700 x 1 + 124
Step 3: We consider the new divisor 700 and the new remainder 124, and apply the division lemma to get
700 = 124 x 5 + 80
We consider the new divisor 124 and the new remainder 80,and apply the division lemma to get
124 = 80 x 1 + 44
We consider the new divisor 80 and the new remainder 44,and apply the division lemma to get
80 = 44 x 1 + 36
We consider the new divisor 44 and the new remainder 36,and apply the division lemma to get
44 = 36 x 1 + 8
We consider the new divisor 36 and the new remainder 8,and apply the division lemma to get
36 = 8 x 4 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 824 and 3172 is 4
Notice that 4 = HCF(8,4) = HCF(36,8) = HCF(44,36) = HCF(80,44) = HCF(124,80) = HCF(700,124) = HCF(824,700) = HCF(3172,824) .
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Frequently Asked Questions on HCF of 824, 3172 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 824, 3172?
Answer: HCF of 824, 3172 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 824, 3172 using Euclid's Algorithm?
Answer: For arbitrary numbers 824, 3172 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.