Highest Common Factor of 615, 993, 706 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, 993, 706 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 615, 993, 706 is 1 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, 993, 706 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, 993, 706 is 1.
HCF(615, 993, 706) = 1
HCF of 615, 993, 706 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, 993, 706 is 1.
Highest Common Factor of 615,993,706 is 1
Step 1: Since 993 > 615, we apply the division lemma to 993 and 615, to get
993 = 615 x 1 + 378
Step 2: Since the reminder 615 ≠ 0, we apply division lemma to 378 and 615, to get
615 = 378 x 1 + 237
Step 3: We consider the new divisor 378 and the new remainder 237, and apply the division lemma to get
378 = 237 x 1 + 141
We consider the new divisor 237 and the new remainder 141,and apply the division lemma to get
237 = 141 x 1 + 96
We consider the new divisor 141 and the new remainder 96,and apply the division lemma to get
141 = 96 x 1 + 45
We consider the new divisor 96 and the new remainder 45,and apply the division lemma to get
96 = 45 x 2 + 6
We consider the new divisor 45 and the new remainder 6,and apply the division lemma to get
45 = 6 x 7 + 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 993 is 3
Notice that 3 = HCF(6,3) = HCF(45,6) = HCF(96,45) = HCF(141,96) = HCF(237,141) = HCF(378,237) = HCF(615,378) = HCF(993,615) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 706 > 3, we apply the division lemma to 706 and 3, to get
706 = 3 x 235 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 706 is 1
Notice that 1 = HCF(3,1) = HCF(706,3) .
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Frequently Asked Questions on HCF of 615, 993, 706 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, 993, 706?
Answer: HCF of 615, 993, 706 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 615, 993, 706 using Euclid's Algorithm?
Answer: For arbitrary numbers 615, 993, 706 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.