Highest Common Factor of 642, 860, 156 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 642, 860, 156 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 642, 860, 156 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, 860, 156 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, 860, 156 is 2.
HCF(642, 860, 156) = 2
HCF of 642, 860, 156 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 642, 860, 156 is 2.
Highest Common Factor of 642,860,156 is 2
Step 1: Since 860 > 642, we apply the division lemma to 860 and 642, to get
860 = 642 x 1 + 218
Step 2: Since the reminder 642 ≠ 0, we apply division lemma to 218 and 642, to get
642 = 218 x 2 + 206
Step 3: We consider the new divisor 218 and the new remainder 206, and apply the division lemma to get
218 = 206 x 1 + 12
We consider the new divisor 206 and the new remainder 12,and apply the division lemma to get
206 = 12 x 17 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 642 and 860 is 2
Notice that 2 = HCF(12,2) = HCF(206,12) = HCF(218,206) = HCF(642,218) = HCF(860,642) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 156 > 2, we apply the division lemma to 156 and 2, to get
156 = 2 x 78 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 156 is 2
Notice that 2 = HCF(156,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 642, 860, 156 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 642, 860, 156?
Answer: HCF of 642, 860, 156 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 642, 860, 156 using Euclid's Algorithm?
Answer: For arbitrary numbers 642, 860, 156 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.