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 689, 21847 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 689, 21847 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 689, 21847 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 689, 21847 is 1.
HCF(689, 21847) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 689, 21847 is 1.
Step 1: Since 21847 > 689, we apply the division lemma to 21847 and 689, to get
21847 = 689 x 31 + 488
Step 2: Since the reminder 689 ≠ 0, we apply division lemma to 488 and 689, to get
689 = 488 x 1 + 201
Step 3: We consider the new divisor 488 and the new remainder 201, and apply the division lemma to get
488 = 201 x 2 + 86
We consider the new divisor 201 and the new remainder 86,and apply the division lemma to get
201 = 86 x 2 + 29
We consider the new divisor 86 and the new remainder 29,and apply the division lemma to get
86 = 29 x 2 + 28
We consider the new divisor 29 and the new remainder 28,and apply the division lemma to get
29 = 28 x 1 + 1
We consider the new divisor 28 and the new remainder 1,and apply the division lemma to get
28 = 1 x 28 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 689 and 21847 is 1
Notice that 1 = HCF(28,1) = HCF(29,28) = HCF(86,29) = HCF(201,86) = HCF(488,201) = HCF(689,488) = HCF(21847,689) .
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 689, 21847?
Answer: HCF of 689, 21847 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 689, 21847 using Euclid's Algorithm?
Answer: For arbitrary numbers 689, 21847 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.