Highest Common Factor of 972, 567, 366 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 972, 567, 366 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 972, 567, 366 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 972, 567, 366 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 972, 567, 366 is 3.
HCF(972, 567, 366) = 3
HCF of 972, 567, 366 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 972, 567, 366 is 3.
Highest Common Factor of 972,567,366 is 3
Step 1: Since 972 > 567, we apply the division lemma to 972 and 567, to get
972 = 567 x 1 + 405
Step 2: Since the reminder 567 ≠ 0, we apply division lemma to 405 and 567, to get
567 = 405 x 1 + 162
Step 3: We consider the new divisor 405 and the new remainder 162, and apply the division lemma to get
405 = 162 x 2 + 81
We consider the new divisor 162 and the new remainder 81, and apply the division lemma to get
162 = 81 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 81, the HCF of 972 and 567 is 81
Notice that 81 = HCF(162,81) = HCF(405,162) = HCF(567,405) = HCF(972,567) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 366 > 81, we apply the division lemma to 366 and 81, to get
366 = 81 x 4 + 42
Step 2: Since the reminder 81 ≠ 0, we apply division lemma to 42 and 81, to get
81 = 42 x 1 + 39
Step 3: We consider the new divisor 42 and the new remainder 39, and apply the division lemma to get
42 = 39 x 1 + 3
We consider the new divisor 39 and the new remainder 3, and apply the division lemma to get
39 = 3 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 81 and 366 is 3
Notice that 3 = HCF(39,3) = HCF(42,39) = HCF(81,42) = HCF(366,81) .
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Frequently Asked Questions on HCF of 972, 567, 366 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 972, 567, 366?
Answer: HCF of 972, 567, 366 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 972, 567, 366 using Euclid's Algorithm?
Answer: For arbitrary numbers 972, 567, 366 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.