Highest Common Factor of 567, 915 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 567, 915 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 567, 915 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 567, 915 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 567, 915 is 3.
HCF(567, 915) = 3
HCF of 567, 915 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 567, 915 is 3.
Highest Common Factor of 567,915 is 3
Step 1: Since 915 > 567, we apply the division lemma to 915 and 567, to get
915 = 567 x 1 + 348
Step 2: Since the reminder 567 ≠ 0, we apply division lemma to 348 and 567, to get
567 = 348 x 1 + 219
Step 3: We consider the new divisor 348 and the new remainder 219, and apply the division lemma to get
348 = 219 x 1 + 129
We consider the new divisor 219 and the new remainder 129,and apply the division lemma to get
219 = 129 x 1 + 90
We consider the new divisor 129 and the new remainder 90,and apply the division lemma to get
129 = 90 x 1 + 39
We consider the new divisor 90 and the new remainder 39,and apply the division lemma to get
90 = 39 x 2 + 12
We consider the new divisor 39 and the new remainder 12,and apply the division lemma to get
39 = 12 x 3 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 567 and 915 is 3
Notice that 3 = HCF(12,3) = HCF(39,12) = HCF(90,39) = HCF(129,90) = HCF(219,129) = HCF(348,219) = HCF(567,348) = HCF(915,567) .
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Frequently Asked Questions on HCF of 567, 915 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 567, 915?
Answer: HCF of 567, 915 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 567, 915 using Euclid's Algorithm?
Answer: For arbitrary numbers 567, 915 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.