Highest Common Factor of 360, 616, 618 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 360, 616, 618 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 360, 616, 618 is 2 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 360, 616, 618 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 360, 616, 618 is 2.
HCF(360, 616, 618) = 2
HCF of 360, 616, 618 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 360, 616, 618 is 2.
Highest Common Factor of 360,616,618 is 2
Step 1: Since 616 > 360, we apply the division lemma to 616 and 360, to get
616 = 360 x 1 + 256
Step 2: Since the reminder 360 ≠ 0, we apply division lemma to 256 and 360, to get
360 = 256 x 1 + 104
Step 3: We consider the new divisor 256 and the new remainder 104, and apply the division lemma to get
256 = 104 x 2 + 48
We consider the new divisor 104 and the new remainder 48,and apply the division lemma to get
104 = 48 x 2 + 8
We consider the new divisor 48 and the new remainder 8,and apply the division lemma to get
48 = 8 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 360 and 616 is 8
Notice that 8 = HCF(48,8) = HCF(104,48) = HCF(256,104) = HCF(360,256) = HCF(616,360) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 618 > 8, we apply the division lemma to 618 and 8, to get
618 = 8 x 77 + 2
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 2 and 8, to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8 and 618 is 2
Notice that 2 = HCF(8,2) = HCF(618,8) .
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Frequently Asked Questions on HCF of 360, 616, 618 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 360, 616, 618?
Answer: HCF of 360, 616, 618 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 360, 616, 618 using Euclid's Algorithm?
Answer: For arbitrary numbers 360, 616, 618 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.