Highest Common Factor of 508, 824 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 508, 824 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 508, 824 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 508, 824 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 508, 824 is 4.
HCF(508, 824) = 4
HCF of 508, 824 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 508, 824 is 4.
Highest Common Factor of 508,824 is 4
Step 1: Since 824 > 508, we apply the division lemma to 824 and 508, to get
824 = 508 x 1 + 316
Step 2: Since the reminder 508 ≠ 0, we apply division lemma to 316 and 508, to get
508 = 316 x 1 + 192
Step 3: We consider the new divisor 316 and the new remainder 192, and apply the division lemma to get
316 = 192 x 1 + 124
We consider the new divisor 192 and the new remainder 124,and apply the division lemma to get
192 = 124 x 1 + 68
We consider the new divisor 124 and the new remainder 68,and apply the division lemma to get
124 = 68 x 1 + 56
We consider the new divisor 68 and the new remainder 56,and apply the division lemma to get
68 = 56 x 1 + 12
We consider the new divisor 56 and the new remainder 12,and apply the division lemma to get
56 = 12 x 4 + 8
We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get
12 = 8 x 1 + 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 508 and 824 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(56,12) = HCF(68,56) = HCF(124,68) = HCF(192,124) = HCF(316,192) = HCF(508,316) = HCF(824,508) .
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Frequently Asked Questions on HCF of 508, 824 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 508, 824?
Answer: HCF of 508, 824 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 508, 824 using Euclid's Algorithm?
Answer: For arbitrary numbers 508, 824 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.