Highest Common Factor of 756, 189, 221 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 756, 189, 221 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 756, 189, 221 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 756, 189, 221 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 756, 189, 221 is 1.
HCF(756, 189, 221) = 1
HCF of 756, 189, 221 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 756, 189, 221 is 1.
Highest Common Factor of 756,189,221 is 1
Step 1: Since 756 > 189, we apply the division lemma to 756 and 189, to get
756 = 189 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 189, the HCF of 756 and 189 is 189
Notice that 189 = HCF(756,189) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 221 > 189, we apply the division lemma to 221 and 189, to get
221 = 189 x 1 + 32
Step 2: Since the reminder 189 ≠ 0, we apply division lemma to 32 and 189, to get
189 = 32 x 5 + 29
Step 3: We consider the new divisor 32 and the new remainder 29, and apply the division lemma to get
32 = 29 x 1 + 3
We consider the new divisor 29 and the new remainder 3,and apply the division lemma to get
29 = 3 x 9 + 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 189 and 221 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(29,3) = HCF(32,29) = HCF(189,32) = HCF(221,189) .
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Frequently Asked Questions on HCF of 756, 189, 221 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 756, 189, 221?
Answer: HCF of 756, 189, 221 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 756, 189, 221 using Euclid's Algorithm?
Answer: For arbitrary numbers 756, 189, 221 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.