Highest Common Factor of 639, 972, 165 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 639, 972, 165 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 639, 972, 165 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 639, 972, 165 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 639, 972, 165 is 3.
HCF(639, 972, 165) = 3
HCF of 639, 972, 165 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 639, 972, 165 is 3.
Highest Common Factor of 639,972,165 is 3
Step 1: Since 972 > 639, we apply the division lemma to 972 and 639, to get
972 = 639 x 1 + 333
Step 2: Since the reminder 639 ≠ 0, we apply division lemma to 333 and 639, to get
639 = 333 x 1 + 306
Step 3: We consider the new divisor 333 and the new remainder 306, and apply the division lemma to get
333 = 306 x 1 + 27
We consider the new divisor 306 and the new remainder 27,and apply the division lemma to get
306 = 27 x 11 + 9
We consider the new divisor 27 and the new remainder 9,and apply the division lemma to get
27 = 9 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 639 and 972 is 9
Notice that 9 = HCF(27,9) = HCF(306,27) = HCF(333,306) = HCF(639,333) = HCF(972,639) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 165 > 9, we apply the division lemma to 165 and 9, to get
165 = 9 x 18 + 3
Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 3 and 9, to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 9 and 165 is 3
Notice that 3 = HCF(9,3) = HCF(165,9) .
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Frequently Asked Questions on HCF of 639, 972, 165 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 639, 972, 165?
Answer: HCF of 639, 972, 165 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 639, 972, 165 using Euclid's Algorithm?
Answer: For arbitrary numbers 639, 972, 165 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.