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 560, 397, 621, 552 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 560, 397, 621, 552 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 560, 397, 621, 552 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 560, 397, 621, 552 is 1.
HCF(560, 397, 621, 552) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 560, 397, 621, 552 is 1.
Step 1: Since 560 > 397, we apply the division lemma to 560 and 397, to get
560 = 397 x 1 + 163
Step 2: Since the reminder 397 ≠ 0, we apply division lemma to 163 and 397, to get
397 = 163 x 2 + 71
Step 3: We consider the new divisor 163 and the new remainder 71, and apply the division lemma to get
163 = 71 x 2 + 21
We consider the new divisor 71 and the new remainder 21,and apply the division lemma to get
71 = 21 x 3 + 8
We consider the new divisor 21 and the new remainder 8,and apply the division lemma to get
21 = 8 x 2 + 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 560 and 397 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(21,8) = HCF(71,21) = HCF(163,71) = HCF(397,163) = HCF(560,397) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 621 > 1, we apply the division lemma to 621 and 1, to get
621 = 1 x 621 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 621 is 1
Notice that 1 = HCF(621,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 552 > 1, we apply the division lemma to 552 and 1, to get
552 = 1 x 552 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 552 is 1
Notice that 1 = HCF(552,1) .
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 560, 397, 621, 552?
Answer: HCF of 560, 397, 621, 552 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 560, 397, 621, 552 using Euclid's Algorithm?
Answer: For arbitrary numbers 560, 397, 621, 552 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.