Highest Common Factor of 640, 998, 60 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 640, 998, 60 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 640, 998, 60 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 640, 998, 60 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 640, 998, 60 is 2.
HCF(640, 998, 60) = 2
HCF of 640, 998, 60 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 640, 998, 60 is 2.
Highest Common Factor of 640,998,60 is 2
Step 1: Since 998 > 640, we apply the division lemma to 998 and 640, to get
998 = 640 x 1 + 358
Step 2: Since the reminder 640 ≠ 0, we apply division lemma to 358 and 640, to get
640 = 358 x 1 + 282
Step 3: We consider the new divisor 358 and the new remainder 282, and apply the division lemma to get
358 = 282 x 1 + 76
We consider the new divisor 282 and the new remainder 76,and apply the division lemma to get
282 = 76 x 3 + 54
We consider the new divisor 76 and the new remainder 54,and apply the division lemma to get
76 = 54 x 1 + 22
We consider the new divisor 54 and the new remainder 22,and apply the division lemma to get
54 = 22 x 2 + 10
We consider the new divisor 22 and the new remainder 10,and apply the division lemma to get
22 = 10 x 2 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 640 and 998 is 2
Notice that 2 = HCF(10,2) = HCF(22,10) = HCF(54,22) = HCF(76,54) = HCF(282,76) = HCF(358,282) = HCF(640,358) = HCF(998,640) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 60 > 2, we apply the division lemma to 60 and 2, to get
60 = 2 x 30 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 60 is 2
Notice that 2 = HCF(60,2) .
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Frequently Asked Questions on HCF of 640, 998, 60 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 640, 998, 60?
Answer: HCF of 640, 998, 60 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 640, 998, 60 using Euclid's Algorithm?
Answer: For arbitrary numbers 640, 998, 60 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.