Highest Common Factor of 417, 670, 123 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 417, 670, 123 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 417, 670, 123 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 417, 670, 123 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 417, 670, 123 is 1.
HCF(417, 670, 123) = 1
HCF of 417, 670, 123 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 417, 670, 123 is 1.
Highest Common Factor of 417,670,123 is 1
Step 1: Since 670 > 417, we apply the division lemma to 670 and 417, to get
670 = 417 x 1 + 253
Step 2: Since the reminder 417 ≠ 0, we apply division lemma to 253 and 417, to get
417 = 253 x 1 + 164
Step 3: We consider the new divisor 253 and the new remainder 164, and apply the division lemma to get
253 = 164 x 1 + 89
We consider the new divisor 164 and the new remainder 89,and apply the division lemma to get
164 = 89 x 1 + 75
We consider the new divisor 89 and the new remainder 75,and apply the division lemma to get
89 = 75 x 1 + 14
We consider the new divisor 75 and the new remainder 14,and apply the division lemma to get
75 = 14 x 5 + 5
We consider the new divisor 14 and the new remainder 5,and apply the division lemma to get
14 = 5 x 2 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 417 and 670 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(14,5) = HCF(75,14) = HCF(89,75) = HCF(164,89) = HCF(253,164) = HCF(417,253) = HCF(670,417) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 123 > 1, we apply the division lemma to 123 and 1, to get
123 = 1 x 123 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 123 is 1
Notice that 1 = HCF(123,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 417, 670, 123 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 417, 670, 123?
Answer: HCF of 417, 670, 123 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 417, 670, 123 using Euclid's Algorithm?
Answer: For arbitrary numbers 417, 670, 123 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.