Highest Common Factor of 616, 440, 18 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 616, 440, 18 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 616, 440, 18 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 616, 440, 18 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 616, 440, 18 is 2.
HCF(616, 440, 18) = 2
HCF of 616, 440, 18 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 616, 440, 18 is 2.
Highest Common Factor of 616,440,18 is 2
Step 1: Since 616 > 440, we apply the division lemma to 616 and 440, to get
616 = 440 x 1 + 176
Step 2: Since the reminder 440 ≠ 0, we apply division lemma to 176 and 440, to get
440 = 176 x 2 + 88
Step 3: We consider the new divisor 176 and the new remainder 88, and apply the division lemma to get
176 = 88 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 88, the HCF of 616 and 440 is 88
Notice that 88 = HCF(176,88) = HCF(440,176) = HCF(616,440) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 88 > 18, we apply the division lemma to 88 and 18, to get
88 = 18 x 4 + 16
Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 16 and 18, to get
18 = 16 x 1 + 2
Step 3: We consider the new divisor 16 and the new remainder 2, and apply the division lemma 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 88 and 18 is 2
Notice that 2 = HCF(16,2) = HCF(18,16) = HCF(88,18) .
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Frequently Asked Questions on HCF of 616, 440, 18 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 616, 440, 18?
Answer: HCF of 616, 440, 18 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 616, 440, 18 using Euclid's Algorithm?
Answer: For arbitrary numbers 616, 440, 18 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
