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 617, 690, 998 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 617, 690, 998 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 617, 690, 998 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 617, 690, 998 is 1.
HCF(617, 690, 998) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 617, 690, 998 is 1.
Step 1: Since 690 > 617, we apply the division lemma to 690 and 617, to get
690 = 617 x 1 + 73
Step 2: Since the reminder 617 ≠ 0, we apply division lemma to 73 and 617, to get
617 = 73 x 8 + 33
Step 3: We consider the new divisor 73 and the new remainder 33, and apply the division lemma to get
73 = 33 x 2 + 7
We consider the new divisor 33 and the new remainder 7,and apply the division lemma to get
33 = 7 x 4 + 5
We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get
7 = 5 x 1 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 617 and 690 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(33,7) = HCF(73,33) = HCF(617,73) = HCF(690,617) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 998 > 1, we apply the division lemma to 998 and 1, to get
998 = 1 x 998 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 998 is 1
Notice that 1 = HCF(998,1) .
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 617, 690, 998?
Answer: HCF of 617, 690, 998 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 617, 690, 998 using Euclid's Algorithm?
Answer: For arbitrary numbers 617, 690, 998 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.