Highest Common Factor of 996, 208 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 996, 208 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 996, 208 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 996, 208 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 996, 208 is 4.
HCF(996, 208) = 4
HCF of 996, 208 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 996, 208 is 4.
Highest Common Factor of 996,208 is 4
Step 1: Since 996 > 208, we apply the division lemma to 996 and 208, to get
996 = 208 x 4 + 164
Step 2: Since the reminder 208 ≠ 0, we apply division lemma to 164 and 208, to get
208 = 164 x 1 + 44
Step 3: We consider the new divisor 164 and the new remainder 44, and apply the division lemma to get
164 = 44 x 3 + 32
We consider the new divisor 44 and the new remainder 32,and apply the division lemma to get
44 = 32 x 1 + 12
We consider the new divisor 32 and the new remainder 12,and apply the division lemma to get
32 = 12 x 2 + 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 996 and 208 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(32,12) = HCF(44,32) = HCF(164,44) = HCF(208,164) = HCF(996,208) .
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Frequently Asked Questions on HCF of 996, 208 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 996, 208?
Answer: HCF of 996, 208 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 996, 208 using Euclid's Algorithm?
Answer: For arbitrary numbers 996, 208 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.