Highest Common Factor of 615, 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 615, 996 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 615, 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 615, 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 615, 996 is 3.
HCF(615, 996) = 3
HCF of 615, 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 615, 996 is 3.
Highest Common Factor of 615,996 is 3
Step 1: Since 996 > 615, we apply the division lemma to 996 and 615, to get
996 = 615 x 1 + 381
Step 2: Since the reminder 615 ≠ 0, we apply division lemma to 381 and 615, to get
615 = 381 x 1 + 234
Step 3: We consider the new divisor 381 and the new remainder 234, and apply the division lemma to get
381 = 234 x 1 + 147
We consider the new divisor 234 and the new remainder 147,and apply the division lemma to get
234 = 147 x 1 + 87
We consider the new divisor 147 and the new remainder 87,and apply the division lemma to get
147 = 87 x 1 + 60
We consider the new divisor 87 and the new remainder 60,and apply the division lemma to get
87 = 60 x 1 + 27
We consider the new divisor 60 and the new remainder 27,and apply the division lemma to get
60 = 27 x 2 + 6
We consider the new divisor 27 and the new remainder 6,and apply the division lemma to get
27 = 6 x 4 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 615 and 996 is 3
Notice that 3 = HCF(6,3) = HCF(27,6) = HCF(60,27) = HCF(87,60) = HCF(147,87) = HCF(234,147) = HCF(381,234) = HCF(615,381) = HCF(996,615) .
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Frequently Asked Questions on HCF of 615, 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 615, 996?
Answer: HCF of 615, 996 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 615, 996 using Euclid's Algorithm?
Answer: For arbitrary numbers 615, 996 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
