Highest Common Factor of 162, 774, 556, 21 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 162, 774, 556, 21 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 162, 774, 556, 21 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 162, 774, 556, 21 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 162, 774, 556, 21 is 1.
HCF(162, 774, 556, 21) = 1
HCF of 162, 774, 556, 21 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 162, 774, 556, 21 is 1.
Highest Common Factor of 162,774,556,21 is 1
Step 1: Since 774 > 162, we apply the division lemma to 774 and 162, to get
774 = 162 x 4 + 126
Step 2: Since the reminder 162 ≠ 0, we apply division lemma to 126 and 162, to get
162 = 126 x 1 + 36
Step 3: We consider the new divisor 126 and the new remainder 36, and apply the division lemma to get
126 = 36 x 3 + 18
We consider the new divisor 36 and the new remainder 18, and apply the division lemma to get
36 = 18 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 162 and 774 is 18
Notice that 18 = HCF(36,18) = HCF(126,36) = HCF(162,126) = HCF(774,162) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 556 > 18, we apply the division lemma to 556 and 18, to get
556 = 18 x 30 + 16
Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 16 and 18, to get
18 = 16 x 1 + 2
Step 3: We consider the new divisor 16 and the new remainder 2, and apply the division lemma to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 18 and 556 is 2
Notice that 2 = HCF(16,2) = HCF(18,16) = HCF(556,18) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 21 > 2, we apply the division lemma to 21 and 2, to get
21 = 2 x 10 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 21 is 1
Notice that 1 = HCF(2,1) = HCF(21,2) .
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Frequently Asked Questions on HCF of 162, 774, 556, 21 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 162, 774, 556, 21?
Answer: HCF of 162, 774, 556, 21 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 162, 774, 556, 21 using Euclid's Algorithm?
Answer: For arbitrary numbers 162, 774, 556, 21 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.