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 842, 622, 178 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 842, 622, 178 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 842, 622, 178 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 842, 622, 178 is 2.
HCF(842, 622, 178) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 842, 622, 178 is 2.
Step 1: Since 842 > 622, we apply the division lemma to 842 and 622, to get
842 = 622 x 1 + 220
Step 2: Since the reminder 622 ≠ 0, we apply division lemma to 220 and 622, to get
622 = 220 x 2 + 182
Step 3: We consider the new divisor 220 and the new remainder 182, and apply the division lemma to get
220 = 182 x 1 + 38
We consider the new divisor 182 and the new remainder 38,and apply the division lemma to get
182 = 38 x 4 + 30
We consider the new divisor 38 and the new remainder 30,and apply the division lemma to get
38 = 30 x 1 + 8
We consider the new divisor 30 and the new remainder 8,and apply the division lemma to get
30 = 8 x 3 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
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 842 and 622 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(30,8) = HCF(38,30) = HCF(182,38) = HCF(220,182) = HCF(622,220) = HCF(842,622) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 178 > 2, we apply the division lemma to 178 and 2, to get
178 = 2 x 89 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 178 is 2
Notice that 2 = HCF(178,2) .
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 842, 622, 178?
Answer: HCF of 842, 622, 178 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 842, 622, 178 using Euclid's Algorithm?
Answer: For arbitrary numbers 842, 622, 178 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.