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 222, 581, 755 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 222, 581, 755 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 222, 581, 755 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 222, 581, 755 is 1.
HCF(222, 581, 755) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 222, 581, 755 is 1.
Step 1: Since 581 > 222, we apply the division lemma to 581 and 222, to get
581 = 222 x 2 + 137
Step 2: Since the reminder 222 ≠ 0, we apply division lemma to 137 and 222, to get
222 = 137 x 1 + 85
Step 3: We consider the new divisor 137 and the new remainder 85, and apply the division lemma to get
137 = 85 x 1 + 52
We consider the new divisor 85 and the new remainder 52,and apply the division lemma to get
85 = 52 x 1 + 33
We consider the new divisor 52 and the new remainder 33,and apply the division lemma to get
52 = 33 x 1 + 19
We consider the new divisor 33 and the new remainder 19,and apply the division lemma to get
33 = 19 x 1 + 14
We consider the new divisor 19 and the new remainder 14,and apply the division lemma to get
19 = 14 x 1 + 5
We consider the new divisor 14 and the new remainder 5,and apply the division lemma to get
14 = 5 x 2 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 222 and 581 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(14,5) = HCF(19,14) = HCF(33,19) = HCF(52,33) = HCF(85,52) = HCF(137,85) = HCF(222,137) = HCF(581,222) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 755 > 1, we apply the division lemma to 755 and 1, to get
755 = 1 x 755 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 755 is 1
Notice that 1 = HCF(755,1) .
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 222, 581, 755?
Answer: HCF of 222, 581, 755 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 222, 581, 755 using Euclid's Algorithm?
Answer: For arbitrary numbers 222, 581, 755 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.