Highest Common Factor of 416, 752, 38, 361 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, 752, 38, 361 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 416, 752, 38, 361 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 416, 752, 38, 361 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, 752, 38, 361 is 1.
HCF(416, 752, 38, 361) = 1
HCF of 416, 752, 38, 361 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, 752, 38, 361 is 1.
Highest Common Factor of 416,752,38,361 is 1
Step 1: Since 752 > 416, we apply the division lemma to 752 and 416, to get
752 = 416 x 1 + 336
Step 2: Since the reminder 416 ≠ 0, we apply division lemma to 336 and 416, to get
416 = 336 x 1 + 80
Step 3: We consider the new divisor 336 and the new remainder 80, and apply the division lemma to get
336 = 80 x 4 + 16
We consider the new divisor 80 and the new remainder 16, and apply the division lemma to get
80 = 16 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 416 and 752 is 16
Notice that 16 = HCF(80,16) = HCF(336,80) = HCF(416,336) = HCF(752,416) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 38 > 16, we apply the division lemma to 38 and 16, to get
38 = 16 x 2 + 6
Step 2: Since the reminder 16 ≠ 0, we apply division lemma to 6 and 16, to get
16 = 6 x 2 + 4
Step 3: We consider the new divisor 6 and the new remainder 4, and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2, and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 16 and 38 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(38,16) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 361 > 2, we apply the division lemma to 361 and 2, to get
361 = 2 x 180 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 361 is 1
Notice that 1 = HCF(2,1) = HCF(361,2) .
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Frequently Asked Questions on HCF of 416, 752, 38, 361 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, 752, 38, 361?
Answer: HCF of 416, 752, 38, 361 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 416, 752, 38, 361 using Euclid's Algorithm?
Answer: For arbitrary numbers 416, 752, 38, 361 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.