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 402, 656, 849 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 402, 656, 849 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 402, 656, 849 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 402, 656, 849 is 1.
HCF(402, 656, 849) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 402, 656, 849 is 1.
Step 1: Since 656 > 402, we apply the division lemma to 656 and 402, to get
656 = 402 x 1 + 254
Step 2: Since the reminder 402 ≠ 0, we apply division lemma to 254 and 402, to get
402 = 254 x 1 + 148
Step 3: We consider the new divisor 254 and the new remainder 148, and apply the division lemma to get
254 = 148 x 1 + 106
We consider the new divisor 148 and the new remainder 106,and apply the division lemma to get
148 = 106 x 1 + 42
We consider the new divisor 106 and the new remainder 42,and apply the division lemma to get
106 = 42 x 2 + 22
We consider the new divisor 42 and the new remainder 22,and apply the division lemma to get
42 = 22 x 1 + 20
We consider the new divisor 22 and the new remainder 20,and apply the division lemma to get
22 = 20 x 1 + 2
We consider the new divisor 20 and the new remainder 2,and apply the division lemma to get
20 = 2 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 402 and 656 is 2
Notice that 2 = HCF(20,2) = HCF(22,20) = HCF(42,22) = HCF(106,42) = HCF(148,106) = HCF(254,148) = HCF(402,254) = HCF(656,402) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 849 > 2, we apply the division lemma to 849 and 2, to get
849 = 2 x 424 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 849 is 1
Notice that 1 = HCF(2,1) = HCF(849,2) .
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 402, 656, 849?
Answer: HCF of 402, 656, 849 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 402, 656, 849 using Euclid's Algorithm?
Answer: For arbitrary numbers 402, 656, 849 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.