Highest Common Factor of 416, 708 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, 708 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 416, 708 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 416, 708 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, 708 is 4.
HCF(416, 708) = 4
HCF of 416, 708 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, 708 is 4.
Highest Common Factor of 416,708 is 4
Step 1: Since 708 > 416, we apply the division lemma to 708 and 416, to get
708 = 416 x 1 + 292
Step 2: Since the reminder 416 ≠ 0, we apply division lemma to 292 and 416, to get
416 = 292 x 1 + 124
Step 3: We consider the new divisor 292 and the new remainder 124, and apply the division lemma to get
292 = 124 x 2 + 44
We consider the new divisor 124 and the new remainder 44,and apply the division lemma to get
124 = 44 x 2 + 36
We consider the new divisor 44 and the new remainder 36,and apply the division lemma to get
44 = 36 x 1 + 8
We consider the new divisor 36 and the new remainder 8,and apply the division lemma to get
36 = 8 x 4 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 416 and 708 is 4
Notice that 4 = HCF(8,4) = HCF(36,8) = HCF(44,36) = HCF(124,44) = HCF(292,124) = HCF(416,292) = HCF(708,416) .
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Frequently Asked Questions on HCF of 416, 708 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, 708?
Answer: HCF of 416, 708 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 416, 708 using Euclid's Algorithm?
Answer: For arbitrary numbers 416, 708 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.