Highest Common Factor of 416, 272, 50 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 416, 272, 50 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 416, 272, 50 is 2 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 416, 272, 50 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 416, 272, 50 is 2.
HCF(416, 272, 50) = 2
HCF of 416, 272, 50 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 416, 272, 50 is 2.
Highest Common Factor of 416,272,50 is 2
Step 1: Since 416 > 272, we apply the division lemma to 416 and 272, to get
416 = 272 x 1 + 144
Step 2: Since the reminder 272 ≠ 0, we apply division lemma to 144 and 272, to get
272 = 144 x 1 + 128
Step 3: We consider the new divisor 144 and the new remainder 128, and apply the division lemma to get
144 = 128 x 1 + 16
We consider the new divisor 128 and the new remainder 16, and apply the division lemma to get
128 = 16 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 416 and 272 is 16
Notice that 16 = HCF(128,16) = HCF(144,128) = HCF(272,144) = HCF(416,272) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 50 > 16, we apply the division lemma to 50 and 16, to get
50 = 16 x 3 + 2
Step 2: Since the reminder 16 ≠ 0, we apply division lemma to 2 and 16, to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 16 and 50 is 2
Notice that 2 = HCF(16,2) = HCF(50,16) .
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Frequently Asked Questions on HCF of 416, 272, 50 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 416, 272, 50?
Answer: HCF of 416, 272, 50 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 416, 272, 50 using Euclid's Algorithm?
Answer: For arbitrary numbers 416, 272, 50 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.