Highest Common Factor of 448, 736, 493 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 448, 736, 493 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 448, 736, 493 is 1 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 448, 736, 493 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 448, 736, 493 is 1.
HCF(448, 736, 493) = 1
HCF of 448, 736, 493 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 448, 736, 493 is 1.
Highest Common Factor of 448,736,493 is 1
Step 1: Since 736 > 448, we apply the division lemma to 736 and 448, to get
736 = 448 x 1 + 288
Step 2: Since the reminder 448 ≠ 0, we apply division lemma to 288 and 448, to get
448 = 288 x 1 + 160
Step 3: We consider the new divisor 288 and the new remainder 160, and apply the division lemma to get
288 = 160 x 1 + 128
We consider the new divisor 160 and the new remainder 128,and apply the division lemma to get
160 = 128 x 1 + 32
We consider the new divisor 128 and the new remainder 32,and apply the division lemma to get
128 = 32 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 32, the HCF of 448 and 736 is 32
Notice that 32 = HCF(128,32) = HCF(160,128) = HCF(288,160) = HCF(448,288) = HCF(736,448) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 493 > 32, we apply the division lemma to 493 and 32, to get
493 = 32 x 15 + 13
Step 2: Since the reminder 32 ≠ 0, we apply division lemma to 13 and 32, to get
32 = 13 x 2 + 6
Step 3: We consider the new divisor 13 and the new remainder 6, and apply the division lemma to get
13 = 6 x 2 + 1
We consider the new divisor 6 and the new remainder 1, and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 32 and 493 is 1
Notice that 1 = HCF(6,1) = HCF(13,6) = HCF(32,13) = HCF(493,32) .
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Frequently Asked Questions on HCF of 448, 736, 493 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 448, 736, 493?
Answer: HCF of 448, 736, 493 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 448, 736, 493 using Euclid's Algorithm?
Answer: For arbitrary numbers 448, 736, 493 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.