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 440, 704, 612, 81 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 440, 704, 612, 81 is 1 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 440, 704, 612, 81 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 440, 704, 612, 81 is 1.
HCF(440, 704, 612, 81) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 440, 704, 612, 81 is 1.
Step 1: Since 704 > 440, we apply the division lemma to 704 and 440, to get
704 = 440 x 1 + 264
Step 2: Since the reminder 440 ≠ 0, we apply division lemma to 264 and 440, to get
440 = 264 x 1 + 176
Step 3: We consider the new divisor 264 and the new remainder 176, and apply the division lemma to get
264 = 176 x 1 + 88
We consider the new divisor 176 and the new remainder 88, and apply the division lemma to get
176 = 88 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 88, the HCF of 440 and 704 is 88
Notice that 88 = HCF(176,88) = HCF(264,176) = HCF(440,264) = HCF(704,440) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 612 > 88, we apply the division lemma to 612 and 88, to get
612 = 88 x 6 + 84
Step 2: Since the reminder 88 ≠ 0, we apply division lemma to 84 and 88, to get
88 = 84 x 1 + 4
Step 3: We consider the new divisor 84 and the new remainder 4, and apply the division lemma to get
84 = 4 x 21 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 88 and 612 is 4
Notice that 4 = HCF(84,4) = HCF(88,84) = HCF(612,88) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 81 > 4, we apply the division lemma to 81 and 4, to get
81 = 4 x 20 + 1
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 81 is 1
Notice that 1 = HCF(4,1) = HCF(81,4) .
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 440, 704, 612, 81?
Answer: HCF of 440, 704, 612, 81 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 440, 704, 612, 81 using Euclid's Algorithm?
Answer: For arbitrary numbers 440, 704, 612, 81 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.