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 162, 606, 769, 713 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 162, 606, 769, 713 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 162, 606, 769, 713 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 162, 606, 769, 713 is 1.
HCF(162, 606, 769, 713) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 162, 606, 769, 713 is 1.
Step 1: Since 606 > 162, we apply the division lemma to 606 and 162, to get
606 = 162 x 3 + 120
Step 2: Since the reminder 162 ≠ 0, we apply division lemma to 120 and 162, to get
162 = 120 x 1 + 42
Step 3: We consider the new divisor 120 and the new remainder 42, and apply the division lemma to get
120 = 42 x 2 + 36
We consider the new divisor 42 and the new remainder 36,and apply the division lemma to get
42 = 36 x 1 + 6
We consider the new divisor 36 and the new remainder 6,and apply the division lemma to get
36 = 6 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 162 and 606 is 6
Notice that 6 = HCF(36,6) = HCF(42,36) = HCF(120,42) = HCF(162,120) = HCF(606,162) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 769 > 6, we apply the division lemma to 769 and 6, to get
769 = 6 x 128 + 1
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 1 and 6, to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6 and 769 is 1
Notice that 1 = HCF(6,1) = HCF(769,6) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 713 > 1, we apply the division lemma to 713 and 1, to get
713 = 1 x 713 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 713 is 1
Notice that 1 = HCF(713,1) .
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 162, 606, 769, 713?
Answer: HCF of 162, 606, 769, 713 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 162, 606, 769, 713 using Euclid's Algorithm?
Answer: For arbitrary numbers 162, 606, 769, 713 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.