Highest Common Factor of 574, 738, 22 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 574, 738, 22 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 574, 738, 22 is 2 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 574, 738, 22 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 574, 738, 22 is 2.
HCF(574, 738, 22) = 2
HCF of 574, 738, 22 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 574, 738, 22 is 2.
Highest Common Factor of 574,738,22 is 2
Step 1: Since 738 > 574, we apply the division lemma to 738 and 574, to get
738 = 574 x 1 + 164
Step 2: Since the reminder 574 ≠ 0, we apply division lemma to 164 and 574, to get
574 = 164 x 3 + 82
Step 3: We consider the new divisor 164 and the new remainder 82, and apply the division lemma to get
164 = 82 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 82, the HCF of 574 and 738 is 82
Notice that 82 = HCF(164,82) = HCF(574,164) = HCF(738,574) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 82 > 22, we apply the division lemma to 82 and 22, to get
82 = 22 x 3 + 16
Step 2: Since the reminder 22 ≠ 0, we apply division lemma to 16 and 22, to get
22 = 16 x 1 + 6
Step 3: We consider the new divisor 16 and the new remainder 6, and apply the division lemma to get
16 = 6 x 2 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 82 and 22 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(22,16) = HCF(82,22) .
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Frequently Asked Questions on HCF of 574, 738, 22 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 574, 738, 22?
Answer: HCF of 574, 738, 22 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 574, 738, 22 using Euclid's Algorithm?
Answer: For arbitrary numbers 574, 738, 22 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.