Highest Common Factor of 354, 564, 537 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 354, 564, 537 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 354, 564, 537 is 3 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 354, 564, 537 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 354, 564, 537 is 3.
HCF(354, 564, 537) = 3
HCF of 354, 564, 537 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 354, 564, 537 is 3.
Highest Common Factor of 354,564,537 is 3
Step 1: Since 564 > 354, we apply the division lemma to 564 and 354, to get
564 = 354 x 1 + 210
Step 2: Since the reminder 354 ≠ 0, we apply division lemma to 210 and 354, to get
354 = 210 x 1 + 144
Step 3: We consider the new divisor 210 and the new remainder 144, and apply the division lemma to get
210 = 144 x 1 + 66
We consider the new divisor 144 and the new remainder 66,and apply the division lemma to get
144 = 66 x 2 + 12
We consider the new divisor 66 and the new remainder 12,and apply the division lemma to get
66 = 12 x 5 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 354 and 564 is 6
Notice that 6 = HCF(12,6) = HCF(66,12) = HCF(144,66) = HCF(210,144) = HCF(354,210) = HCF(564,354) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 537 > 6, we apply the division lemma to 537 and 6, to get
537 = 6 x 89 + 3
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 3 and 6, to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 6 and 537 is 3
Notice that 3 = HCF(6,3) = HCF(537,6) .
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Frequently Asked Questions on HCF of 354, 564, 537 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 354, 564, 537?
Answer: HCF of 354, 564, 537 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 354, 564, 537 using Euclid's Algorithm?
Answer: For arbitrary numbers 354, 564, 537 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.