Highest Common Factor of 667, 120, 642 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 667, 120, 642 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 667, 120, 642 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 667, 120, 642 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 667, 120, 642 is 1.
HCF(667, 120, 642) = 1
HCF of 667, 120, 642 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 667, 120, 642 is 1.
Highest Common Factor of 667,120,642 is 1
Step 1: Since 667 > 120, we apply the division lemma to 667 and 120, to get
667 = 120 x 5 + 67
Step 2: Since the reminder 120 ≠ 0, we apply division lemma to 67 and 120, to get
120 = 67 x 1 + 53
Step 3: We consider the new divisor 67 and the new remainder 53, and apply the division lemma to get
67 = 53 x 1 + 14
We consider the new divisor 53 and the new remainder 14,and apply the division lemma to get
53 = 14 x 3 + 11
We consider the new divisor 14 and the new remainder 11,and apply the division lemma to get
14 = 11 x 1 + 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 667 and 120 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(14,11) = HCF(53,14) = HCF(67,53) = HCF(120,67) = HCF(667,120) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 642 > 1, we apply the division lemma to 642 and 1, to get
642 = 1 x 642 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 642 is 1
Notice that 1 = HCF(642,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 667, 120, 642 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 667, 120, 642?
Answer: HCF of 667, 120, 642 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 667, 120, 642 using Euclid's Algorithm?
Answer: For arbitrary numbers 667, 120, 642 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.