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 613, 517, 907, 74 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 613, 517, 907, 74 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 613, 517, 907, 74 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 613, 517, 907, 74 is 1.
HCF(613, 517, 907, 74) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 613, 517, 907, 74 is 1.
Step 1: Since 613 > 517, we apply the division lemma to 613 and 517, to get
613 = 517 x 1 + 96
Step 2: Since the reminder 517 ≠ 0, we apply division lemma to 96 and 517, to get
517 = 96 x 5 + 37
Step 3: We consider the new divisor 96 and the new remainder 37, and apply the division lemma to get
96 = 37 x 2 + 22
We consider the new divisor 37 and the new remainder 22,and apply the division lemma to get
37 = 22 x 1 + 15
We consider the new divisor 22 and the new remainder 15,and apply the division lemma to get
22 = 15 x 1 + 7
We consider the new divisor 15 and the new remainder 7,and apply the division lemma to get
15 = 7 x 2 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 613 and 517 is 1
Notice that 1 = HCF(7,1) = HCF(15,7) = HCF(22,15) = HCF(37,22) = HCF(96,37) = HCF(517,96) = HCF(613,517) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 907 > 1, we apply the division lemma to 907 and 1, to get
907 = 1 x 907 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 907 is 1
Notice that 1 = HCF(907,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 74 > 1, we apply the division lemma to 74 and 1, to get
74 = 1 x 74 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 74 is 1
Notice that 1 = HCF(74,1) .
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 613, 517, 907, 74?
Answer: HCF of 613, 517, 907, 74 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 613, 517, 907, 74 using Euclid's Algorithm?
Answer: For arbitrary numbers 613, 517, 907, 74 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.