Highest Common Factor of 615, 855, 910 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, 855, 910 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 615, 855, 910 is 5 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, 855, 910 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, 855, 910 is 5.
HCF(615, 855, 910) = 5
HCF of 615, 855, 910 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, 855, 910 is 5.
Highest Common Factor of 615,855,910 is 5
Step 1: Since 855 > 615, we apply the division lemma to 855 and 615, to get
855 = 615 x 1 + 240
Step 2: Since the reminder 615 ≠ 0, we apply division lemma to 240 and 615, to get
615 = 240 x 2 + 135
Step 3: We consider the new divisor 240 and the new remainder 135, and apply the division lemma to get
240 = 135 x 1 + 105
We consider the new divisor 135 and the new remainder 105,and apply the division lemma to get
135 = 105 x 1 + 30
We consider the new divisor 105 and the new remainder 30,and apply the division lemma to get
105 = 30 x 3 + 15
We consider the new divisor 30 and the new remainder 15,and apply the division lemma to get
30 = 15 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 615 and 855 is 15
Notice that 15 = HCF(30,15) = HCF(105,30) = HCF(135,105) = HCF(240,135) = HCF(615,240) = HCF(855,615) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 910 > 15, we apply the division lemma to 910 and 15, to get
910 = 15 x 60 + 10
Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 10 and 15, to get
15 = 10 x 1 + 5
Step 3: We consider the new divisor 10 and the new remainder 5, and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 15 and 910 is 5
Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(910,15) .
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Frequently Asked Questions on HCF of 615, 855, 910 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, 855, 910?
Answer: HCF of 615, 855, 910 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 615, 855, 910 using Euclid's Algorithm?
Answer: For arbitrary numbers 615, 855, 910 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.