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 361, 562, 997 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 361, 562, 997 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 361, 562, 997 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 361, 562, 997 is 1.
HCF(361, 562, 997) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 361, 562, 997 is 1.
Step 1: Since 562 > 361, we apply the division lemma to 562 and 361, to get
562 = 361 x 1 + 201
Step 2: Since the reminder 361 ≠ 0, we apply division lemma to 201 and 361, to get
361 = 201 x 1 + 160
Step 3: We consider the new divisor 201 and the new remainder 160, and apply the division lemma to get
201 = 160 x 1 + 41
We consider the new divisor 160 and the new remainder 41,and apply the division lemma to get
160 = 41 x 3 + 37
We consider the new divisor 41 and the new remainder 37,and apply the division lemma to get
41 = 37 x 1 + 4
We consider the new divisor 37 and the new remainder 4,and apply the division lemma to get
37 = 4 x 9 + 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 361 and 562 is 1
Notice that 1 = HCF(4,1) = HCF(37,4) = HCF(41,37) = HCF(160,41) = HCF(201,160) = HCF(361,201) = HCF(562,361) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 997 > 1, we apply the division lemma to 997 and 1, to get
997 = 1 x 997 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 997 is 1
Notice that 1 = HCF(997,1) .
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 361, 562, 997?
Answer: HCF of 361, 562, 997 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 361, 562, 997 using Euclid's Algorithm?
Answer: For arbitrary numbers 361, 562, 997 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.