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 849, 9670 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 849, 9670 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 849, 9670 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 849, 9670 is 1.
HCF(849, 9670) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 849, 9670 is 1.
Step 1: Since 9670 > 849, we apply the division lemma to 9670 and 849, to get
9670 = 849 x 11 + 331
Step 2: Since the reminder 849 ≠ 0, we apply division lemma to 331 and 849, to get
849 = 331 x 2 + 187
Step 3: We consider the new divisor 331 and the new remainder 187, and apply the division lemma to get
331 = 187 x 1 + 144
We consider the new divisor 187 and the new remainder 144,and apply the division lemma to get
187 = 144 x 1 + 43
We consider the new divisor 144 and the new remainder 43,and apply the division lemma to get
144 = 43 x 3 + 15
We consider the new divisor 43 and the new remainder 15,and apply the division lemma to get
43 = 15 x 2 + 13
We consider the new divisor 15 and the new remainder 13,and apply the division lemma to get
15 = 13 x 1 + 2
We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get
13 = 2 x 6 + 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 849 and 9670 is 1
Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(15,13) = HCF(43,15) = HCF(144,43) = HCF(187,144) = HCF(331,187) = HCF(849,331) = HCF(9670,849) .
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 849, 9670?
Answer: HCF of 849, 9670 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 849, 9670 using Euclid's Algorithm?
Answer: For arbitrary numbers 849, 9670 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.