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 573, 977, 340 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 573, 977, 340 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 573, 977, 340 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 573, 977, 340 is 1.
HCF(573, 977, 340) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 573, 977, 340 is 1.
Step 1: Since 977 > 573, we apply the division lemma to 977 and 573, to get
977 = 573 x 1 + 404
Step 2: Since the reminder 573 ≠ 0, we apply division lemma to 404 and 573, to get
573 = 404 x 1 + 169
Step 3: We consider the new divisor 404 and the new remainder 169, and apply the division lemma to get
404 = 169 x 2 + 66
We consider the new divisor 169 and the new remainder 66,and apply the division lemma to get
169 = 66 x 2 + 37
We consider the new divisor 66 and the new remainder 37,and apply the division lemma to get
66 = 37 x 1 + 29
We consider the new divisor 37 and the new remainder 29,and apply the division lemma to get
37 = 29 x 1 + 8
We consider the new divisor 29 and the new remainder 8,and apply the division lemma to get
29 = 8 x 3 + 5
We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get
8 = 5 x 1 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 573 and 977 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(29,8) = HCF(37,29) = HCF(66,37) = HCF(169,66) = HCF(404,169) = HCF(573,404) = HCF(977,573) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 340 > 1, we apply the division lemma to 340 and 1, to get
340 = 1 x 340 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 340 is 1
Notice that 1 = HCF(340,1) .
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 573, 977, 340?
Answer: HCF of 573, 977, 340 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 573, 977, 340 using Euclid's Algorithm?
Answer: For arbitrary numbers 573, 977, 340 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.