Highest Common Factor of 336, 616, 510 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 336, 616, 510 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 336, 616, 510 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 336, 616, 510 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 336, 616, 510 is 2.
HCF(336, 616, 510) = 2
HCF of 336, 616, 510 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 336, 616, 510 is 2.
Highest Common Factor of 336,616,510 is 2
Step 1: Since 616 > 336, we apply the division lemma to 616 and 336, to get
616 = 336 x 1 + 280
Step 2: Since the reminder 336 ≠ 0, we apply division lemma to 280 and 336, to get
336 = 280 x 1 + 56
Step 3: We consider the new divisor 280 and the new remainder 56, and apply the division lemma to get
280 = 56 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 56, the HCF of 336 and 616 is 56
Notice that 56 = HCF(280,56) = HCF(336,280) = HCF(616,336) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 510 > 56, we apply the division lemma to 510 and 56, to get
510 = 56 x 9 + 6
Step 2: Since the reminder 56 ≠ 0, we apply division lemma to 6 and 56, to get
56 = 6 x 9 + 2
Step 3: We consider the new divisor 6 and the new remainder 2, and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 56 and 510 is 2
Notice that 2 = HCF(6,2) = HCF(56,6) = HCF(510,56) .
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Frequently Asked Questions on HCF of 336, 616, 510 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 336, 616, 510?
Answer: HCF of 336, 616, 510 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 336, 616, 510 using Euclid's Algorithm?
Answer: For arbitrary numbers 336, 616, 510 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
