Highest Common Factor of 461, 416, 31 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 461, 416, 31 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 461, 416, 31 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 461, 416, 31 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 461, 416, 31 is 1.
HCF(461, 416, 31) = 1
HCF of 461, 416, 31 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 461, 416, 31 is 1.
Highest Common Factor of 461,416,31 is 1
Step 1: Since 461 > 416, we apply the division lemma to 461 and 416, to get
461 = 416 x 1 + 45
Step 2: Since the reminder 416 ≠ 0, we apply division lemma to 45 and 416, to get
416 = 45 x 9 + 11
Step 3: We consider the new divisor 45 and the new remainder 11, and apply the division lemma to get
45 = 11 x 4 + 1
We consider the new divisor 11 and the new remainder 1, and apply the division lemma to get
11 = 1 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 461 and 416 is 1
Notice that 1 = HCF(11,1) = HCF(45,11) = HCF(416,45) = HCF(461,416) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 31 > 1, we apply the division lemma to 31 and 1, to get
31 = 1 x 31 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 31 is 1
Notice that 1 = HCF(31,1) .
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Frequently Asked Questions on HCF of 461, 416, 31 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 461, 416, 31?
Answer: HCF of 461, 416, 31 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 461, 416, 31 using Euclid's Algorithm?
Answer: For arbitrary numbers 461, 416, 31 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.