Highest Common Factor of 63, 294, 435 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 63, 294, 435 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 63, 294, 435 is 3 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 63, 294, 435 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 63, 294, 435 is 3.
HCF(63, 294, 435) = 3
HCF of 63, 294, 435 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 63, 294, 435 is 3.
Highest Common Factor of 63,294,435 is 3
Step 1: Since 294 > 63, we apply the division lemma to 294 and 63, to get
294 = 63 x 4 + 42
Step 2: Since the reminder 63 ≠ 0, we apply division lemma to 42 and 63, to get
63 = 42 x 1 + 21
Step 3: We consider the new divisor 42 and the new remainder 21, and apply the division lemma to get
42 = 21 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 21, the HCF of 63 and 294 is 21
Notice that 21 = HCF(42,21) = HCF(63,42) = HCF(294,63) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 435 > 21, we apply the division lemma to 435 and 21, to get
435 = 21 x 20 + 15
Step 2: Since the reminder 21 ≠ 0, we apply division lemma to 15 and 21, to get
21 = 15 x 1 + 6
Step 3: We consider the new divisor 15 and the new remainder 6, and apply the division lemma to get
15 = 6 x 2 + 3
We consider the new divisor 6 and the new remainder 3, and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 21 and 435 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(21,15) = HCF(435,21) .
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Frequently Asked Questions on HCF of 63, 294, 435 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 63, 294, 435?
Answer: HCF of 63, 294, 435 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 63, 294, 435 using Euclid's Algorithm?
Answer: For arbitrary numbers 63, 294, 435 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.