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 705, 765, 967 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 705, 765, 967 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 705, 765, 967 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 705, 765, 967 is 1.
HCF(705, 765, 967) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 705, 765, 967 is 1.
Step 1: Since 765 > 705, we apply the division lemma to 765 and 705, to get
765 = 705 x 1 + 60
Step 2: Since the reminder 705 ≠ 0, we apply division lemma to 60 and 705, to get
705 = 60 x 11 + 45
Step 3: We consider the new divisor 60 and the new remainder 45, and apply the division lemma to get
60 = 45 x 1 + 15
We consider the new divisor 45 and the new remainder 15, and apply the division lemma to get
45 = 15 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 705 and 765 is 15
Notice that 15 = HCF(45,15) = HCF(60,45) = HCF(705,60) = HCF(765,705) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 967 > 15, we apply the division lemma to 967 and 15, to get
967 = 15 x 64 + 7
Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 7 and 15, to get
15 = 7 x 2 + 1
Step 3: We consider the new divisor 7 and the new remainder 1, and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 15 and 967 is 1
Notice that 1 = HCF(7,1) = HCF(15,7) = HCF(967,15) .
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 705, 765, 967?
Answer: HCF of 705, 765, 967 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 705, 765, 967 using Euclid's Algorithm?
Answer: For arbitrary numbers 705, 765, 967 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.