Highest Common Factor of 653, 846, 762 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, 846, 762 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 653, 846, 762 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, 846, 762 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, 846, 762 is 1.
HCF(653, 846, 762) = 1
HCF of 653, 846, 762 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, 846, 762 is 1.
Highest Common Factor of 653,846,762 is 1
Step 1: Since 846 > 653, we apply the division lemma to 846 and 653, to get
846 = 653 x 1 + 193
Step 2: Since the reminder 653 ≠ 0, we apply division lemma to 193 and 653, to get
653 = 193 x 3 + 74
Step 3: We consider the new divisor 193 and the new remainder 74, and apply the division lemma to get
193 = 74 x 2 + 45
We consider the new divisor 74 and the new remainder 45,and apply the division lemma to get
74 = 45 x 1 + 29
We consider the new divisor 45 and the new remainder 29,and apply the division lemma to get
45 = 29 x 1 + 16
We consider the new divisor 29 and the new remainder 16,and apply the division lemma to get
29 = 16 x 1 + 13
We consider the new divisor 16 and the new remainder 13,and apply the division lemma to get
16 = 13 x 1 + 3
We consider the new divisor 13 and the new remainder 3,and apply the division lemma to get
13 = 3 x 4 + 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 846 is 1
Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(16,13) = HCF(29,16) = HCF(45,29) = HCF(74,45) = HCF(193,74) = HCF(653,193) = HCF(846,653) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 762 > 1, we apply the division lemma to 762 and 1, to get
762 = 1 x 762 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 762 is 1
Notice that 1 = HCF(762,1) .
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Frequently Asked Questions on HCF of 653, 846, 762 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, 846, 762?
Answer: HCF of 653, 846, 762 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 653, 846, 762 using Euclid's Algorithm?
Answer: For arbitrary numbers 653, 846, 762 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
