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 642, 786, 908 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 642, 786, 908 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 642, 786, 908 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 642, 786, 908 is 2.
HCF(642, 786, 908) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 642, 786, 908 is 2.
Step 1: Since 786 > 642, we apply the division lemma to 786 and 642, to get
786 = 642 x 1 + 144
Step 2: Since the reminder 642 ≠ 0, we apply division lemma to 144 and 642, to get
642 = 144 x 4 + 66
Step 3: We consider the new divisor 144 and the new remainder 66, and apply the division lemma to get
144 = 66 x 2 + 12
We consider the new divisor 66 and the new remainder 12,and apply the division lemma to get
66 = 12 x 5 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 642 and 786 is 6
Notice that 6 = HCF(12,6) = HCF(66,12) = HCF(144,66) = HCF(642,144) = HCF(786,642) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 908 > 6, we apply the division lemma to 908 and 6, to get
908 = 6 x 151 + 2
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 2 and 6, 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 6 and 908 is 2
Notice that 2 = HCF(6,2) = HCF(908,6) .
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 642, 786, 908?
Answer: HCF of 642, 786, 908 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 642, 786, 908 using Euclid's Algorithm?
Answer: For arbitrary numbers 642, 786, 908 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.