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 722, 585, 402 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 722, 585, 402 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 722, 585, 402 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 722, 585, 402 is 1.
HCF(722, 585, 402) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 722, 585, 402 is 1.
Step 1: Since 722 > 585, we apply the division lemma to 722 and 585, to get
722 = 585 x 1 + 137
Step 2: Since the reminder 585 ≠ 0, we apply division lemma to 137 and 585, to get
585 = 137 x 4 + 37
Step 3: We consider the new divisor 137 and the new remainder 37, and apply the division lemma to get
137 = 37 x 3 + 26
We consider the new divisor 37 and the new remainder 26,and apply the division lemma to get
37 = 26 x 1 + 11
We consider the new divisor 26 and the new remainder 11,and apply the division lemma to get
26 = 11 x 2 + 4
We consider the new divisor 11 and the new remainder 4,and apply the division lemma to get
11 = 4 x 2 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 722 and 585 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(26,11) = HCF(37,26) = HCF(137,37) = HCF(585,137) = HCF(722,585) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 402 > 1, we apply the division lemma to 402 and 1, to get
402 = 1 x 402 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 402 is 1
Notice that 1 = HCF(402,1) .
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 722, 585, 402?
Answer: HCF of 722, 585, 402 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 722, 585, 402 using Euclid's Algorithm?
Answer: For arbitrary numbers 722, 585, 402 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.