Highest Common Factor of 972, 339, 786 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, 339, 786 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 972, 339, 786 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, 339, 786 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, 339, 786 is 3.
HCF(972, 339, 786) = 3
HCF of 972, 339, 786 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, 339, 786 is 3.
Highest Common Factor of 972,339,786 is 3
Step 1: Since 972 > 339, we apply the division lemma to 972 and 339, to get
972 = 339 x 2 + 294
Step 2: Since the reminder 339 ≠ 0, we apply division lemma to 294 and 339, to get
339 = 294 x 1 + 45
Step 3: We consider the new divisor 294 and the new remainder 45, and apply the division lemma to get
294 = 45 x 6 + 24
We consider the new divisor 45 and the new remainder 24,and apply the division lemma to get
45 = 24 x 1 + 21
We consider the new divisor 24 and the new remainder 21,and apply the division lemma to get
24 = 21 x 1 + 3
We consider the new divisor 21 and the new remainder 3,and apply the division lemma to get
21 = 3 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 972 and 339 is 3
Notice that 3 = HCF(21,3) = HCF(24,21) = HCF(45,24) = HCF(294,45) = HCF(339,294) = HCF(972,339) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 786 > 3, we apply the division lemma to 786 and 3, to get
786 = 3 x 262 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 786 is 3
Notice that 3 = HCF(786,3) .
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Frequently Asked Questions on HCF of 972, 339, 786 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, 339, 786?
Answer: HCF of 972, 339, 786 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 972, 339, 786 using Euclid's Algorithm?
Answer: For arbitrary numbers 972, 339, 786 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.