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 438, 729, 456 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 438, 729, 456 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 438, 729, 456 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 438, 729, 456 is 3.
HCF(438, 729, 456) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 438, 729, 456 is 3.
Step 1: Since 729 > 438, we apply the division lemma to 729 and 438, to get
729 = 438 x 1 + 291
Step 2: Since the reminder 438 ≠ 0, we apply division lemma to 291 and 438, to get
438 = 291 x 1 + 147
Step 3: We consider the new divisor 291 and the new remainder 147, and apply the division lemma to get
291 = 147 x 1 + 144
We consider the new divisor 147 and the new remainder 144,and apply the division lemma to get
147 = 144 x 1 + 3
We consider the new divisor 144 and the new remainder 3,and apply the division lemma to get
144 = 3 x 48 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 438 and 729 is 3
Notice that 3 = HCF(144,3) = HCF(147,144) = HCF(291,147) = HCF(438,291) = HCF(729,438) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 456 > 3, we apply the division lemma to 456 and 3, to get
456 = 3 x 152 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 456 is 3
Notice that 3 = HCF(456,3) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 438, 729, 456?
Answer: HCF of 438, 729, 456 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 438, 729, 456 using Euclid's Algorithm?
Answer: For arbitrary numbers 438, 729, 456 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.