Highest Common Factor of 782, 306, 448 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 782, 306, 448 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 782, 306, 448 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 782, 306, 448 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 782, 306, 448 is 2.
HCF(782, 306, 448) = 2
HCF of 782, 306, 448 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 782, 306, 448 is 2.
Highest Common Factor of 782,306,448 is 2
Step 1: Since 782 > 306, we apply the division lemma to 782 and 306, to get
782 = 306 x 2 + 170
Step 2: Since the reminder 306 ≠ 0, we apply division lemma to 170 and 306, to get
306 = 170 x 1 + 136
Step 3: We consider the new divisor 170 and the new remainder 136, and apply the division lemma to get
170 = 136 x 1 + 34
We consider the new divisor 136 and the new remainder 34, and apply the division lemma to get
136 = 34 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 34, the HCF of 782 and 306 is 34
Notice that 34 = HCF(136,34) = HCF(170,136) = HCF(306,170) = HCF(782,306) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 448 > 34, we apply the division lemma to 448 and 34, to get
448 = 34 x 13 + 6
Step 2: Since the reminder 34 ≠ 0, we apply division lemma to 6 and 34, to get
34 = 6 x 5 + 4
Step 3: We consider the new divisor 6 and the new remainder 4, and apply the division lemma to get
6 = 4 x 1 + 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 34 and 448 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(34,6) = HCF(448,34) .
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Frequently Asked Questions on HCF of 782, 306, 448 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 782, 306, 448?
Answer: HCF of 782, 306, 448 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 782, 306, 448 using Euclid's Algorithm?
Answer: For arbitrary numbers 782, 306, 448 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.