Highest Common Factor of 240, 160, 221, 572 using Euclid's algorithm
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 240, 160, 221, 572 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 240, 160, 221, 572 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 240, 160, 221, 572 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 240, 160, 221, 572 is 1.
HCF(240, 160, 221, 572) = 1
HCF of 240, 160, 221, 572 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 240, 160, 221, 572 is 1.
Highest Common Factor of 240,160,221,572 is 1
Step 1: Since 240 > 160, we apply the division lemma to 240 and 160, to get
240 = 160 x 1 + 80
Step 2: Since the reminder 160 ≠ 0, we apply division lemma to 80 and 160, to get
160 = 80 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 80, the HCF of 240 and 160 is 80
Notice that 80 = HCF(160,80) = HCF(240,160) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 221 > 80, we apply the division lemma to 221 and 80, to get
221 = 80 x 2 + 61
Step 2: Since the reminder 80 ≠ 0, we apply division lemma to 61 and 80, to get
80 = 61 x 1 + 19
Step 3: We consider the new divisor 61 and the new remainder 19, and apply the division lemma to get
61 = 19 x 3 + 4
We consider the new divisor 19 and the new remainder 4,and apply the division lemma to get
19 = 4 x 4 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 80 and 221 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(19,4) = HCF(61,19) = HCF(80,61) = HCF(221,80) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 572 > 1, we apply the division lemma to 572 and 1, to get
572 = 1 x 572 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 572 is 1
Notice that 1 = HCF(572,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 240, 160, 221, 572 using Euclid's Algorithm
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 240, 160, 221, 572?
Answer: HCF of 240, 160, 221, 572 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 240, 160, 221, 572 using Euclid's Algorithm?
Answer: For arbitrary numbers 240, 160, 221, 572 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.