Highest Common Factor of 312, 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 312, 824 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 312, 824 is 8 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 312, 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 312, 824 is 8.
HCF(312, 824) = 8
HCF of 312, 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 312, 824 is 8.
Highest Common Factor of 312,824 is 8
Step 1: Since 824 > 312, we apply the division lemma to 824 and 312, to get
824 = 312 x 2 + 200
Step 2: Since the reminder 312 ≠ 0, we apply division lemma to 200 and 312, to get
312 = 200 x 1 + 112
Step 3: We consider the new divisor 200 and the new remainder 112, and apply the division lemma to get
200 = 112 x 1 + 88
We consider the new divisor 112 and the new remainder 88,and apply the division lemma to get
112 = 88 x 1 + 24
We consider the new divisor 88 and the new remainder 24,and apply the division lemma to get
88 = 24 x 3 + 16
We consider the new divisor 24 and the new remainder 16,and apply the division lemma to get
24 = 16 x 1 + 8
We consider the new divisor 16 and the new remainder 8,and apply the division lemma to get
16 = 8 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 312 and 824 is 8
Notice that 8 = HCF(16,8) = HCF(24,16) = HCF(88,24) = HCF(112,88) = HCF(200,112) = HCF(312,200) = HCF(824,312) .
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Frequently Asked Questions on HCF of 312, 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 312, 824?
Answer: HCF of 312, 824 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 312, 824 using Euclid's Algorithm?
Answer: For arbitrary numbers 312, 824 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.