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 704, 3040, 8767 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 704, 3040, 8767 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 704, 3040, 8767 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 704, 3040, 8767 is 1.
HCF(704, 3040, 8767) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 704, 3040, 8767 is 1.
Step 1: Since 3040 > 704, we apply the division lemma to 3040 and 704, to get
3040 = 704 x 4 + 224
Step 2: Since the reminder 704 ≠ 0, we apply division lemma to 224 and 704, to get
704 = 224 x 3 + 32
Step 3: We consider the new divisor 224 and the new remainder 32, and apply the division lemma to get
224 = 32 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 32, the HCF of 704 and 3040 is 32
Notice that 32 = HCF(224,32) = HCF(704,224) = HCF(3040,704) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8767 > 32, we apply the division lemma to 8767 and 32, to get
8767 = 32 x 273 + 31
Step 2: Since the reminder 32 ≠ 0, we apply division lemma to 31 and 32, to get
32 = 31 x 1 + 1
Step 3: We consider the new divisor 31 and the new remainder 1, and apply the division lemma to get
31 = 1 x 31 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 32 and 8767 is 1
Notice that 1 = HCF(31,1) = HCF(32,31) = HCF(8767,32) .
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 704, 3040, 8767?
Answer: HCF of 704, 3040, 8767 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 704, 3040, 8767 using Euclid's Algorithm?
Answer: For arbitrary numbers 704, 3040, 8767 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.