Highest Common Factor of 546, 630, 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 546, 630, 448 i.e. 14 the largest integer that leaves a remainder zero for all numbers.
HCF of 546, 630, 448 is 14 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 546, 630, 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 546, 630, 448 is 14.
HCF(546, 630, 448) = 14
HCF of 546, 630, 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 546, 630, 448 is 14.
Highest Common Factor of 546,630,448 is 14
Step 1: Since 630 > 546, we apply the division lemma to 630 and 546, to get
630 = 546 x 1 + 84
Step 2: Since the reminder 546 ≠ 0, we apply division lemma to 84 and 546, to get
546 = 84 x 6 + 42
Step 3: We consider the new divisor 84 and the new remainder 42, and apply the division lemma to get
84 = 42 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 42, the HCF of 546 and 630 is 42
Notice that 42 = HCF(84,42) = HCF(546,84) = HCF(630,546) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 448 > 42, we apply the division lemma to 448 and 42, to get
448 = 42 x 10 + 28
Step 2: Since the reminder 42 ≠ 0, we apply division lemma to 28 and 42, to get
42 = 28 x 1 + 14
Step 3: We consider the new divisor 28 and the new remainder 14, and apply the division lemma to get
28 = 14 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 42 and 448 is 14
Notice that 14 = HCF(28,14) = HCF(42,28) = HCF(448,42) .
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Frequently Asked Questions on HCF of 546, 630, 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 546, 630, 448?
Answer: HCF of 546, 630, 448 is 14 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 546, 630, 448 using Euclid's Algorithm?
Answer: For arbitrary numbers 546, 630, 448 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.