Highest Common Factor of 472, 649, 65, 109 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 472, 649, 65, 109 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 472, 649, 65, 109 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 472, 649, 65, 109 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 472, 649, 65, 109 is 1.
HCF(472, 649, 65, 109) = 1
HCF of 472, 649, 65, 109 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 472, 649, 65, 109 is 1.
Highest Common Factor of 472,649,65,109 is 1
Step 1: Since 649 > 472, we apply the division lemma to 649 and 472, to get
649 = 472 x 1 + 177
Step 2: Since the reminder 472 ≠ 0, we apply division lemma to 177 and 472, to get
472 = 177 x 2 + 118
Step 3: We consider the new divisor 177 and the new remainder 118, and apply the division lemma to get
177 = 118 x 1 + 59
We consider the new divisor 118 and the new remainder 59, and apply the division lemma to get
118 = 59 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 59, the HCF of 472 and 649 is 59
Notice that 59 = HCF(118,59) = HCF(177,118) = HCF(472,177) = HCF(649,472) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 65 > 59, we apply the division lemma to 65 and 59, to get
65 = 59 x 1 + 6
Step 2: Since the reminder 59 ≠ 0, we apply division lemma to 6 and 59, to get
59 = 6 x 9 + 5
Step 3: We consider the new divisor 6 and the new remainder 5, and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1, and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 59 and 65 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(59,6) = HCF(65,59) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 109 > 1, we apply the division lemma to 109 and 1, to get
109 = 1 x 109 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 109 is 1
Notice that 1 = HCF(109,1) .
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Frequently Asked Questions on HCF of 472, 649, 65, 109 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 472, 649, 65, 109?
Answer: HCF of 472, 649, 65, 109 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 472, 649, 65, 109 using Euclid's Algorithm?
Answer: For arbitrary numbers 472, 649, 65, 109 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
