Highest Common Factor of 708, 448, 358 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, 448, 358 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 708, 448, 358 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 708, 448, 358 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, 448, 358 is 2.
HCF(708, 448, 358) = 2
HCF of 708, 448, 358 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, 448, 358 is 2.
Highest Common Factor of 708,448,358 is 2
Step 1: Since 708 > 448, we apply the division lemma to 708 and 448, to get
708 = 448 x 1 + 260
Step 2: Since the reminder 448 ≠ 0, we apply division lemma to 260 and 448, to get
448 = 260 x 1 + 188
Step 3: We consider the new divisor 260 and the new remainder 188, and apply the division lemma to get
260 = 188 x 1 + 72
We consider the new divisor 188 and the new remainder 72,and apply the division lemma to get
188 = 72 x 2 + 44
We consider the new divisor 72 and the new remainder 44,and apply the division lemma to get
72 = 44 x 1 + 28
We consider the new divisor 44 and the new remainder 28,and apply the division lemma to get
44 = 28 x 1 + 16
We consider the new divisor 28 and the new remainder 16,and apply the division lemma to get
28 = 16 x 1 + 12
We consider the new divisor 16 and the new remainder 12,and apply the division lemma to get
16 = 12 x 1 + 4
We consider the new divisor 12 and the new remainder 4,and apply the division lemma to get
12 = 4 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 708 and 448 is 4
Notice that 4 = HCF(12,4) = HCF(16,12) = HCF(28,16) = HCF(44,28) = HCF(72,44) = HCF(188,72) = HCF(260,188) = HCF(448,260) = HCF(708,448) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 358 > 4, we apply the division lemma to 358 and 4, to get
358 = 4 x 89 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4 and 358 is 2
Notice that 2 = HCF(4,2) = HCF(358,4) .
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Frequently Asked Questions on HCF of 708, 448, 358 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, 448, 358?
Answer: HCF of 708, 448, 358 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 708, 448, 358 using Euclid's Algorithm?
Answer: For arbitrary numbers 708, 448, 358 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.