Highest Common Factor of 621, 996 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 621, 996 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 621, 996 is 3 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 621, 996 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 621, 996 is 3.
HCF(621, 996) = 3
HCF of 621, 996 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 621, 996 is 3.
Highest Common Factor of 621,996 is 3
Step 1: Since 996 > 621, we apply the division lemma to 996 and 621, to get
996 = 621 x 1 + 375
Step 2: Since the reminder 621 ≠ 0, we apply division lemma to 375 and 621, to get
621 = 375 x 1 + 246
Step 3: We consider the new divisor 375 and the new remainder 246, and apply the division lemma to get
375 = 246 x 1 + 129
We consider the new divisor 246 and the new remainder 129,and apply the division lemma to get
246 = 129 x 1 + 117
We consider the new divisor 129 and the new remainder 117,and apply the division lemma to get
129 = 117 x 1 + 12
We consider the new divisor 117 and the new remainder 12,and apply the division lemma to get
117 = 12 x 9 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 621 and 996 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(117,12) = HCF(129,117) = HCF(246,129) = HCF(375,246) = HCF(621,375) = HCF(996,621) .
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Frequently Asked Questions on HCF of 621, 996 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 621, 996?
Answer: HCF of 621, 996 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 621, 996 using Euclid's Algorithm?
Answer: For arbitrary numbers 621, 996 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.