Highest Common Factor of 708, 615 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 708, 615 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 708, 615 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 708, 615 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 708, 615 is 3.
HCF(708, 615) = 3
HCF of 708, 615 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 708, 615 is 3.
Highest Common Factor of 708,615 is 3
Step 1: Since 708 > 615, we apply the division lemma to 708 and 615, to get
708 = 615 x 1 + 93
Step 2: Since the reminder 615 ≠ 0, we apply division lemma to 93 and 615, to get
615 = 93 x 6 + 57
Step 3: We consider the new divisor 93 and the new remainder 57, and apply the division lemma to get
93 = 57 x 1 + 36
We consider the new divisor 57 and the new remainder 36,and apply the division lemma to get
57 = 36 x 1 + 21
We consider the new divisor 36 and the new remainder 21,and apply the division lemma to get
36 = 21 x 1 + 15
We consider the new divisor 21 and the new remainder 15,and apply the division lemma to get
21 = 15 x 1 + 6
We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get
15 = 6 x 2 + 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 708 and 615 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(21,15) = HCF(36,21) = HCF(57,36) = HCF(93,57) = HCF(615,93) = HCF(708,615) .
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Frequently Asked Questions on HCF of 708, 615 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 708, 615?
Answer: HCF of 708, 615 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 708, 615 using Euclid's Algorithm?
Answer: For arbitrary numbers 708, 615 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.