Highest Common Factor of 672, 285, 969 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 672, 285, 969 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 672, 285, 969 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 672, 285, 969 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 672, 285, 969 is 3.
HCF(672, 285, 969) = 3
HCF of 672, 285, 969 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 672, 285, 969 is 3.
Highest Common Factor of 672,285,969 is 3
Step 1: Since 672 > 285, we apply the division lemma to 672 and 285, to get
672 = 285 x 2 + 102
Step 2: Since the reminder 285 ≠ 0, we apply division lemma to 102 and 285, to get
285 = 102 x 2 + 81
Step 3: We consider the new divisor 102 and the new remainder 81, and apply the division lemma to get
102 = 81 x 1 + 21
We consider the new divisor 81 and the new remainder 21,and apply the division lemma to get
81 = 21 x 3 + 18
We consider the new divisor 21 and the new remainder 18,and apply the division lemma to get
21 = 18 x 1 + 3
We consider the new divisor 18 and the new remainder 3,and apply the division lemma to get
18 = 3 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 672 and 285 is 3
Notice that 3 = HCF(18,3) = HCF(21,18) = HCF(81,21) = HCF(102,81) = HCF(285,102) = HCF(672,285) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 969 > 3, we apply the division lemma to 969 and 3, to get
969 = 3 x 323 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 969 is 3
Notice that 3 = HCF(969,3) .
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Frequently Asked Questions on HCF of 672, 285, 969 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 672, 285, 969?
Answer: HCF of 672, 285, 969 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 672, 285, 969 using Euclid's Algorithm?
Answer: For arbitrary numbers 672, 285, 969 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.