Highest Common Factor of 653, 906 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 653, 906 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 653, 906 is 1 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 653, 906 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 653, 906 is 1.
HCF(653, 906) = 1
HCF of 653, 906 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 653, 906 is 1.
Highest Common Factor of 653,906 is 1
Step 1: Since 906 > 653, we apply the division lemma to 906 and 653, to get
906 = 653 x 1 + 253
Step 2: Since the reminder 653 ≠ 0, we apply division lemma to 253 and 653, to get
653 = 253 x 2 + 147
Step 3: We consider the new divisor 253 and the new remainder 147, and apply the division lemma to get
253 = 147 x 1 + 106
We consider the new divisor 147 and the new remainder 106,and apply the division lemma to get
147 = 106 x 1 + 41
We consider the new divisor 106 and the new remainder 41,and apply the division lemma to get
106 = 41 x 2 + 24
We consider the new divisor 41 and the new remainder 24,and apply the division lemma to get
41 = 24 x 1 + 17
We consider the new divisor 24 and the new remainder 17,and apply the division lemma to get
24 = 17 x 1 + 7
We consider the new divisor 17 and the new remainder 7,and apply the division lemma to get
17 = 7 x 2 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 653 and 906 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(17,7) = HCF(24,17) = HCF(41,24) = HCF(106,41) = HCF(147,106) = HCF(253,147) = HCF(653,253) = HCF(906,653) .
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Frequently Asked Questions on HCF of 653, 906 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 653, 906?
Answer: HCF of 653, 906 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 653, 906 using Euclid's Algorithm?
Answer: For arbitrary numbers 653, 906 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.