Highest Common Factor of 488, 840, 622 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 488, 840, 622 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 488, 840, 622 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 488, 840, 622 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 488, 840, 622 is 2.
HCF(488, 840, 622) = 2
HCF of 488, 840, 622 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 488, 840, 622 is 2.
Highest Common Factor of 488,840,622 is 2
Step 1: Since 840 > 488, we apply the division lemma to 840 and 488, to get
840 = 488 x 1 + 352
Step 2: Since the reminder 488 ≠ 0, we apply division lemma to 352 and 488, to get
488 = 352 x 1 + 136
Step 3: We consider the new divisor 352 and the new remainder 136, and apply the division lemma to get
352 = 136 x 2 + 80
We consider the new divisor 136 and the new remainder 80,and apply the division lemma to get
136 = 80 x 1 + 56
We consider the new divisor 80 and the new remainder 56,and apply the division lemma to get
80 = 56 x 1 + 24
We consider the new divisor 56 and the new remainder 24,and apply the division lemma to get
56 = 24 x 2 + 8
We consider the new divisor 24 and the new remainder 8,and apply the division lemma to get
24 = 8 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 488 and 840 is 8
Notice that 8 = HCF(24,8) = HCF(56,24) = HCF(80,56) = HCF(136,80) = HCF(352,136) = HCF(488,352) = HCF(840,488) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 622 > 8, we apply the division lemma to 622 and 8, to get
622 = 8 x 77 + 6
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 6 and 8, to get
8 = 6 x 1 + 2
Step 3: We consider the new divisor 6 and the new remainder 2, and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8 and 622 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(622,8) .
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Frequently Asked Questions on HCF of 488, 840, 622 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 488, 840, 622?
Answer: HCF of 488, 840, 622 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 488, 840, 622 using Euclid's Algorithm?
Answer: For arbitrary numbers 488, 840, 622 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.