Highest Common Factor of 360, 224, 765 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, 224, 765 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 360, 224, 765 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 360, 224, 765 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, 224, 765 is 1.
HCF(360, 224, 765) = 1
HCF of 360, 224, 765 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, 224, 765 is 1.
Highest Common Factor of 360,224,765 is 1
Step 1: Since 360 > 224, we apply the division lemma to 360 and 224, to get
360 = 224 x 1 + 136
Step 2: Since the reminder 224 ≠ 0, we apply division lemma to 136 and 224, to get
224 = 136 x 1 + 88
Step 3: We consider the new divisor 136 and the new remainder 88, and apply the division lemma to get
136 = 88 x 1 + 48
We consider the new divisor 88 and the new remainder 48,and apply the division lemma to get
88 = 48 x 1 + 40
We consider the new divisor 48 and the new remainder 40,and apply the division lemma to get
48 = 40 x 1 + 8
We consider the new divisor 40 and the new remainder 8,and apply the division lemma to get
40 = 8 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 360 and 224 is 8
Notice that 8 = HCF(40,8) = HCF(48,40) = HCF(88,48) = HCF(136,88) = HCF(224,136) = HCF(360,224) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 765 > 8, we apply the division lemma to 765 and 8, to get
765 = 8 x 95 + 5
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 5 and 8, to get
8 = 5 x 1 + 3
Step 3: We consider the new divisor 5 and the new remainder 3, and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8 and 765 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(765,8) .
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Frequently Asked Questions on HCF of 360, 224, 765 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, 224, 765?
Answer: HCF of 360, 224, 765 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 360, 224, 765 using Euclid's Algorithm?
Answer: For arbitrary numbers 360, 224, 765 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.