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, 490, 662 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 849, 490, 662 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, 490, 662 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, 490, 662 is 1.
HCF(849, 490, 662) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 849, 490, 662 is 1.
Step 1: Since 849 > 490, we apply the division lemma to 849 and 490, to get
849 = 490 x 1 + 359
Step 2: Since the reminder 490 ≠ 0, we apply division lemma to 359 and 490, to get
490 = 359 x 1 + 131
Step 3: We consider the new divisor 359 and the new remainder 131, and apply the division lemma to get
359 = 131 x 2 + 97
We consider the new divisor 131 and the new remainder 97,and apply the division lemma to get
131 = 97 x 1 + 34
We consider the new divisor 97 and the new remainder 34,and apply the division lemma to get
97 = 34 x 2 + 29
We consider the new divisor 34 and the new remainder 29,and apply the division lemma to get
34 = 29 x 1 + 5
We consider the new divisor 29 and the new remainder 5,and apply the division lemma to get
29 = 5 x 5 + 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 849 and 490 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(29,5) = HCF(34,29) = HCF(97,34) = HCF(131,97) = HCF(359,131) = HCF(490,359) = HCF(849,490) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 662 > 1, we apply the division lemma to 662 and 1, to get
662 = 1 x 662 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 662 is 1
Notice that 1 = HCF(662,1) .
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 849, 490, 662?
Answer: HCF of 849, 490, 662 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 849, 490, 662 using Euclid's Algorithm?
Answer: For arbitrary numbers 849, 490, 662 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.