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 670, 421, 639 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 670, 421, 639 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 670, 421, 639 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 670, 421, 639 is 1.
HCF(670, 421, 639) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 670, 421, 639 is 1.
Step 1: Since 670 > 421, we apply the division lemma to 670 and 421, to get
670 = 421 x 1 + 249
Step 2: Since the reminder 421 ≠ 0, we apply division lemma to 249 and 421, to get
421 = 249 x 1 + 172
Step 3: We consider the new divisor 249 and the new remainder 172, and apply the division lemma to get
249 = 172 x 1 + 77
We consider the new divisor 172 and the new remainder 77,and apply the division lemma to get
172 = 77 x 2 + 18
We consider the new divisor 77 and the new remainder 18,and apply the division lemma to get
77 = 18 x 4 + 5
We consider the new divisor 18 and the new remainder 5,and apply the division lemma to get
18 = 5 x 3 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 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 670 and 421 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(18,5) = HCF(77,18) = HCF(172,77) = HCF(249,172) = HCF(421,249) = HCF(670,421) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 639 > 1, we apply the division lemma to 639 and 1, to get
639 = 1 x 639 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 639 is 1
Notice that 1 = HCF(639,1) .
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 670, 421, 639?
Answer: HCF of 670, 421, 639 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 670, 421, 639 using Euclid's Algorithm?
Answer: For arbitrary numbers 670, 421, 639 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.