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 662, 4382, 6054 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 662, 4382, 6054 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 662, 4382, 6054 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 662, 4382, 6054 is 2.
HCF(662, 4382, 6054) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 662, 4382, 6054 is 2.
Step 1: Since 4382 > 662, we apply the division lemma to 4382 and 662, to get
4382 = 662 x 6 + 410
Step 2: Since the reminder 662 ≠ 0, we apply division lemma to 410 and 662, to get
662 = 410 x 1 + 252
Step 3: We consider the new divisor 410 and the new remainder 252, and apply the division lemma to get
410 = 252 x 1 + 158
We consider the new divisor 252 and the new remainder 158,and apply the division lemma to get
252 = 158 x 1 + 94
We consider the new divisor 158 and the new remainder 94,and apply the division lemma to get
158 = 94 x 1 + 64
We consider the new divisor 94 and the new remainder 64,and apply the division lemma to get
94 = 64 x 1 + 30
We consider the new divisor 64 and the new remainder 30,and apply the division lemma to get
64 = 30 x 2 + 4
We consider the new divisor 30 and the new remainder 4,and apply the division lemma to get
30 = 4 x 7 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 662 and 4382 is 2
Notice that 2 = HCF(4,2) = HCF(30,4) = HCF(64,30) = HCF(94,64) = HCF(158,94) = HCF(252,158) = HCF(410,252) = HCF(662,410) = HCF(4382,662) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 6054 > 2, we apply the division lemma to 6054 and 2, to get
6054 = 2 x 3027 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 6054 is 2
Notice that 2 = HCF(6054,2) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 662, 4382, 6054?
Answer: HCF of 662, 4382, 6054 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 662, 4382, 6054 using Euclid's Algorithm?
Answer: For arbitrary numbers 662, 4382, 6054 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.