Highest Common Factor of 708, 916, 316 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 708, 916, 316 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 708, 916, 316 is 4 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 708, 916, 316 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 708, 916, 316 is 4.
HCF(708, 916, 316) = 4
HCF of 708, 916, 316 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 708, 916, 316 is 4.
Highest Common Factor of 708,916,316 is 4
Step 1: Since 916 > 708, we apply the division lemma to 916 and 708, to get
916 = 708 x 1 + 208
Step 2: Since the reminder 708 ≠ 0, we apply division lemma to 208 and 708, to get
708 = 208 x 3 + 84
Step 3: We consider the new divisor 208 and the new remainder 84, and apply the division lemma to get
208 = 84 x 2 + 40
We consider the new divisor 84 and the new remainder 40,and apply the division lemma to get
84 = 40 x 2 + 4
We consider the new divisor 40 and the new remainder 4,and apply the division lemma to get
40 = 4 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 708 and 916 is 4
Notice that 4 = HCF(40,4) = HCF(84,40) = HCF(208,84) = HCF(708,208) = HCF(916,708) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 316 > 4, we apply the division lemma to 316 and 4, to get
316 = 4 x 79 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 316 is 4
Notice that 4 = HCF(316,4) .
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Frequently Asked Questions on HCF of 708, 916, 316 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 708, 916, 316?
Answer: HCF of 708, 916, 316 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 708, 916, 316 using Euclid's Algorithm?
Answer: For arbitrary numbers 708, 916, 316 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.