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, 992, 730 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 617, 992, 730 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, 992, 730 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, 992, 730 is 1.
HCF(617, 992, 730) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 617, 992, 730 is 1.
Step 1: Since 992 > 617, we apply the division lemma to 992 and 617, to get
992 = 617 x 1 + 375
Step 2: Since the reminder 617 ≠ 0, we apply division lemma to 375 and 617, to get
617 = 375 x 1 + 242
Step 3: We consider the new divisor 375 and the new remainder 242, and apply the division lemma to get
375 = 242 x 1 + 133
We consider the new divisor 242 and the new remainder 133,and apply the division lemma to get
242 = 133 x 1 + 109
We consider the new divisor 133 and the new remainder 109,and apply the division lemma to get
133 = 109 x 1 + 24
We consider the new divisor 109 and the new remainder 24,and apply the division lemma to get
109 = 24 x 4 + 13
We consider the new divisor 24 and the new remainder 13,and apply the division lemma to get
24 = 13 x 1 + 11
We consider the new divisor 13 and the new remainder 11,and apply the division lemma to get
13 = 11 x 1 + 2
We consider the new divisor 11 and the new remainder 2,and apply the division lemma to get
11 = 2 x 5 + 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 992 is 1
Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(13,11) = HCF(24,13) = HCF(109,24) = HCF(133,109) = HCF(242,133) = HCF(375,242) = HCF(617,375) = HCF(992,617) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 730 > 1, we apply the division lemma to 730 and 1, to get
730 = 1 x 730 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 730 is 1
Notice that 1 = HCF(730,1) .
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, 992, 730?
Answer: HCF of 617, 992, 730 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 617, 992, 730 using Euclid's Algorithm?
Answer: For arbitrary numbers 617, 992, 730 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.