Highest Common Factor of 356, 572, 574, 66 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 356, 572, 574, 66 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 356, 572, 574, 66 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 356, 572, 574, 66 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 356, 572, 574, 66 is 2.
HCF(356, 572, 574, 66) = 2
HCF of 356, 572, 574, 66 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 356, 572, 574, 66 is 2.
Highest Common Factor of 356,572,574,66 is 2
Step 1: Since 572 > 356, we apply the division lemma to 572 and 356, to get
572 = 356 x 1 + 216
Step 2: Since the reminder 356 ≠ 0, we apply division lemma to 216 and 356, to get
356 = 216 x 1 + 140
Step 3: We consider the new divisor 216 and the new remainder 140, and apply the division lemma to get
216 = 140 x 1 + 76
We consider the new divisor 140 and the new remainder 76,and apply the division lemma to get
140 = 76 x 1 + 64
We consider the new divisor 76 and the new remainder 64,and apply the division lemma to get
76 = 64 x 1 + 12
We consider the new divisor 64 and the new remainder 12,and apply the division lemma to get
64 = 12 x 5 + 4
We consider the new divisor 12 and the new remainder 4,and apply the division lemma to get
12 = 4 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 356 and 572 is 4
Notice that 4 = HCF(12,4) = HCF(64,12) = HCF(76,64) = HCF(140,76) = HCF(216,140) = HCF(356,216) = HCF(572,356) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 574 > 4, we apply the division lemma to 574 and 4, to get
574 = 4 x 143 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, 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 4 and 574 is 2
Notice that 2 = HCF(4,2) = HCF(574,4) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 66 > 2, we apply the division lemma to 66 and 2, to get
66 = 2 x 33 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 66 is 2
Notice that 2 = HCF(66,2) .
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Frequently Asked Questions on HCF of 356, 572, 574, 66 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 356, 572, 574, 66?
Answer: HCF of 356, 572, 574, 66 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 356, 572, 574, 66 using Euclid's Algorithm?
Answer: For arbitrary numbers 356, 572, 574, 66 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.