Highest Common Factor of 22, 77, 42 using Euclid's algorithm
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 22, 77, 42 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 22, 77, 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 22, 77, 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 22, 77, 42 is 1.
HCF(22, 77, 42) = 1
HCF of 22, 77, 42 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 22, 77, 42 is 1.
Highest Common Factor of 22,77,42 is 1
Step 1: Since 77 > 22, we apply the division lemma to 77 and 22, to get
77 = 22 x 3 + 11
Step 2: Since the reminder 22 ≠ 0, we apply division lemma to 11 and 22, to get
22 = 11 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 22 and 77 is 11
Notice that 11 = HCF(22,11) = HCF(77,22) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 42 > 11, we apply the division lemma to 42 and 11, to get
42 = 11 x 3 + 9
Step 2: Since the reminder 11 ≠ 0, we apply division lemma to 9 and 11, to get
11 = 9 x 1 + 2
Step 3: We consider the new divisor 9 and the new remainder 2, and apply the division lemma to get
9 = 2 x 4 + 1
We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 11 and 42 is 1
Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(11,9) = HCF(42,11) .
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Frequently Asked Questions on HCF of 22, 77, 42 using Euclid's Algorithm
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 22, 77, 42?
Answer: HCF of 22, 77, 42 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 22, 77, 42 using Euclid's Algorithm?
Answer: For arbitrary numbers 22, 77, 42 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.