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 658, 423, 340 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 658, 423, 340 is 1 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 658, 423, 340 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 658, 423, 340 is 1.
HCF(658, 423, 340) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 658, 423, 340 is 1.
Step 1: Since 658 > 423, we apply the division lemma to 658 and 423, to get
658 = 423 x 1 + 235
Step 2: Since the reminder 423 ≠ 0, we apply division lemma to 235 and 423, to get
423 = 235 x 1 + 188
Step 3: We consider the new divisor 235 and the new remainder 188, and apply the division lemma to get
235 = 188 x 1 + 47
We consider the new divisor 188 and the new remainder 47, and apply the division lemma to get
188 = 47 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 47, the HCF of 658 and 423 is 47
Notice that 47 = HCF(188,47) = HCF(235,188) = HCF(423,235) = HCF(658,423) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 340 > 47, we apply the division lemma to 340 and 47, to get
340 = 47 x 7 + 11
Step 2: Since the reminder 47 ≠ 0, we apply division lemma to 11 and 47, to get
47 = 11 x 4 + 3
Step 3: We consider the new divisor 11 and the new remainder 3, and apply the division lemma to get
11 = 3 x 3 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 47 and 340 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(47,11) = HCF(340,47) .
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 658, 423, 340?
Answer: HCF of 658, 423, 340 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 658, 423, 340 using Euclid's Algorithm?
Answer: For arbitrary numbers 658, 423, 340 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.