Highest Common Factor of 416, 640, 216 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, 640, 216 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 416, 640, 216 is 8 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, 640, 216 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, 640, 216 is 8.
HCF(416, 640, 216) = 8
HCF of 416, 640, 216 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, 640, 216 is 8.
Highest Common Factor of 416,640,216 is 8
Step 1: Since 640 > 416, we apply the division lemma to 640 and 416, to get
640 = 416 x 1 + 224
Step 2: Since the reminder 416 ≠ 0, we apply division lemma to 224 and 416, to get
416 = 224 x 1 + 192
Step 3: We consider the new divisor 224 and the new remainder 192, and apply the division lemma to get
224 = 192 x 1 + 32
We consider the new divisor 192 and the new remainder 32, and apply the division lemma to get
192 = 32 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 32, the HCF of 416 and 640 is 32
Notice that 32 = HCF(192,32) = HCF(224,192) = HCF(416,224) = HCF(640,416) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 216 > 32, we apply the division lemma to 216 and 32, to get
216 = 32 x 6 + 24
Step 2: Since the reminder 32 ≠ 0, we apply division lemma to 24 and 32, to get
32 = 24 x 1 + 8
Step 3: We consider the new divisor 24 and the new remainder 8, and apply the division lemma to get
24 = 8 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 32 and 216 is 8
Notice that 8 = HCF(24,8) = HCF(32,24) = HCF(216,32) .
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Frequently Asked Questions on HCF of 416, 640, 216 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, 640, 216?
Answer: HCF of 416, 640, 216 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 416, 640, 216 using Euclid's Algorithm?
Answer: For arbitrary numbers 416, 640, 216 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.