Highest Common Factor of 894, 645 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 894, 645 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 894, 645 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 894, 645 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 894, 645 is 3.
HCF(894, 645) = 3
HCF of 894, 645 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 894, 645 is 3.
Highest Common Factor of 894,645 is 3
Step 1: Since 894 > 645, we apply the division lemma to 894 and 645, to get
894 = 645 x 1 + 249
Step 2: Since the reminder 645 ≠ 0, we apply division lemma to 249 and 645, to get
645 = 249 x 2 + 147
Step 3: We consider the new divisor 249 and the new remainder 147, and apply the division lemma to get
249 = 147 x 1 + 102
We consider the new divisor 147 and the new remainder 102,and apply the division lemma to get
147 = 102 x 1 + 45
We consider the new divisor 102 and the new remainder 45,and apply the division lemma to get
102 = 45 x 2 + 12
We consider the new divisor 45 and the new remainder 12,and apply the division lemma to get
45 = 12 x 3 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma 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 894 and 645 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(45,12) = HCF(102,45) = HCF(147,102) = HCF(249,147) = HCF(645,249) = HCF(894,645) .
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Frequently Asked Questions on HCF of 894, 645 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 894, 645?
Answer: HCF of 894, 645 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 894, 645 using Euclid's Algorithm?
Answer: For arbitrary numbers 894, 645 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.