Highest Common Factor of 736, 480, 178 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 736, 480, 178 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 736, 480, 178 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 736, 480, 178 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 736, 480, 178 is 2.
HCF(736, 480, 178) = 2
HCF of 736, 480, 178 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 736, 480, 178 is 2.
Highest Common Factor of 736,480,178 is 2
Step 1: Since 736 > 480, we apply the division lemma to 736 and 480, to get
736 = 480 x 1 + 256
Step 2: Since the reminder 480 ≠ 0, we apply division lemma to 256 and 480, to get
480 = 256 x 1 + 224
Step 3: We consider the new divisor 256 and the new remainder 224, and apply the division lemma to get
256 = 224 x 1 + 32
We consider the new divisor 224 and the new remainder 32, and apply the division lemma to get
224 = 32 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 32, the HCF of 736 and 480 is 32
Notice that 32 = HCF(224,32) = HCF(256,224) = HCF(480,256) = HCF(736,480) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 178 > 32, we apply the division lemma to 178 and 32, to get
178 = 32 x 5 + 18
Step 2: Since the reminder 32 ≠ 0, we apply division lemma to 18 and 32, to get
32 = 18 x 1 + 14
Step 3: We consider the new divisor 18 and the new remainder 14, and apply the division lemma to get
18 = 14 x 1 + 4
We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get
14 = 4 x 3 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma 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 32 and 178 is 2
Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(18,14) = HCF(32,18) = HCF(178,32) .
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Frequently Asked Questions on HCF of 736, 480, 178 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 736, 480, 178?
Answer: HCF of 736, 480, 178 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 736, 480, 178 using Euclid's Algorithm?
Answer: For arbitrary numbers 736, 480, 178 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.