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 661, 827, 42 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 661, 827, 42 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 661, 827, 42 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 661, 827, 42 is 1.
HCF(661, 827, 42) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 661, 827, 42 is 1.
Step 1: Since 827 > 661, we apply the division lemma to 827 and 661, to get
827 = 661 x 1 + 166
Step 2: Since the reminder 661 ≠ 0, we apply division lemma to 166 and 661, to get
661 = 166 x 3 + 163
Step 3: We consider the new divisor 166 and the new remainder 163, and apply the division lemma to get
166 = 163 x 1 + 3
We consider the new divisor 163 and the new remainder 3,and apply the division lemma to get
163 = 3 x 54 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 661 and 827 is 1
Notice that 1 = HCF(3,1) = HCF(163,3) = HCF(166,163) = HCF(661,166) = HCF(827,661) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 42 > 1, we apply the division lemma to 42 and 1, to get
42 = 1 x 42 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 42 is 1
Notice that 1 = HCF(42,1) .
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 661, 827, 42?
Answer: HCF of 661, 827, 42 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 661, 827, 42 using Euclid's Algorithm?
Answer: For arbitrary numbers 661, 827, 42 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.