Highest Common Factor of 918, 560, 640 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 918, 560, 640 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 918, 560, 640 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 918, 560, 640 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 918, 560, 640 is 2.
HCF(918, 560, 640) = 2
HCF of 918, 560, 640 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 918, 560, 640 is 2.
Highest Common Factor of 918,560,640 is 2
Step 1: Since 918 > 560, we apply the division lemma to 918 and 560, to get
918 = 560 x 1 + 358
Step 2: Since the reminder 560 ≠ 0, we apply division lemma to 358 and 560, to get
560 = 358 x 1 + 202
Step 3: We consider the new divisor 358 and the new remainder 202, and apply the division lemma to get
358 = 202 x 1 + 156
We consider the new divisor 202 and the new remainder 156,and apply the division lemma to get
202 = 156 x 1 + 46
We consider the new divisor 156 and the new remainder 46,and apply the division lemma to get
156 = 46 x 3 + 18
We consider the new divisor 46 and the new remainder 18,and apply the division lemma to get
46 = 18 x 2 + 10
We consider the new divisor 18 and the new remainder 10,and apply the division lemma to get
18 = 10 x 1 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma 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 918 and 560 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(18,10) = HCF(46,18) = HCF(156,46) = HCF(202,156) = HCF(358,202) = HCF(560,358) = HCF(918,560) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 640 > 2, we apply the division lemma to 640 and 2, to get
640 = 2 x 320 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 640 is 2
Notice that 2 = HCF(640,2) .
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Frequently Asked Questions on HCF of 918, 560, 640 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 918, 560, 640?
Answer: HCF of 918, 560, 640 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 918, 560, 640 using Euclid's Algorithm?
Answer: For arbitrary numbers 918, 560, 640 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.